The Dongsithouane National Production Forest (DNPF) is one of the largest natural forest areas in Savannakhet, Lao PDR, which has been a vital support for the local community’s livelihood, Recently, significant chang...The Dongsithouane National Production Forest (DNPF) is one of the largest natural forest areas in Savannakhet, Lao PDR, which has been a vital support for the local community’s livelihood, Recently, significant changes in land use and land cover (LULC) have been observed in this area, leading to a reduction of natural forests. There were two separate methods of this study: firstly, to identify LULC changes across three different periods, spectral imagery from the Landsat 5 Thematic Mapper (TM) for the years 2001 and 2011, and the Landsat 8 Operational Land Imager (OLI) for 2021 were used as the primary data sources. The satellite images were preprocessed for various forest classes, including pretreatment of the top of atmosphere reflectance by using QGIS software’s semi-automatic classification plug-in (SCP), and ArcGIS was used for post-classification. A supervised classification approach was applied to the satellite images from 2001, 2011, and 2021 to generate diverse maps of LULC. Secondly, a household survey dataset was used to investigate influential factors. Approximately 220 households were interviewed in order to collect socio-economic information (including data on population growth, increased business activities, location of the area, agriculture land expansion, and need for settlement land). Household survey data was analyzed by using SPSS. Descriptive statistics, including frequency distributions and percentages, were applied to observe characteristics. Additionally, a binary logistic regression model was used to analyze the socioeconomic factors related to LULC change in DNPF. Key findings indicated a decline in natural forest areas within the study site. Specifically, both dry dipterocarp forest (−11.35%) and mixed deciduous forest (−0.18%) decreased from 2001 to 2021. The overall accuracy of the LULC maps was 94%, 86%, and 89% for the years 2001, 2011, and 2021 respectively. In contrast, agricultural land increased significantly by 155.70%, while built-up land, and water bodies increased by 65.54% and 35.33%, respectively. The results also highlighted a significant increase in construction land, up to 65.54%. Furthermore, the study found a correlation between agricultural expansion and a reduction of forest areas, along with an increase in built-up land along the forest areas’ boundaries. Timber exploitation and charcoal production also contributed to the decline in forest cover. The logistic regression model identified significant determinants of LULC change, including the area’s location, agricultural land expansion, increased business activity, and the need for settlement land. These factors have influenced the management of DNPF. Urgent sustainable management practices and actions, including forest ecosystem protection, village agricultural zoning, water source and watershed protection and public awareness, are required to preserve the forest areas of DNPF.展开更多
A numerical model has been developed for simulating land-surface processes and atmospheric boundary layer climate of vegetation and desert in semi-arid region.Dynamically,thermal and hydrological processes take place ...A numerical model has been developed for simulating land-surface processes and atmospheric boundary layer climate of vegetation and desert in semi-arid region.Dynamically,thermal and hydrological processes take place in the atmospheric boundary layer.Vegetation and surface layer of soil are included in the soil-vegetation-atmosphere coupled system,in which,vegetation is considered as a horizontally uniform layer,soil is divided into 13 layers and the horizontal differences of variables in the system are neglected.The influence of local boundary layer climate by vegetation cover factor is simulated with the coupled model in the semi-arid region of Northwest China (around 38°N,105°E).Results indicate that due to significant differences of water and energy budgets in vegetation and desert region,the air is colder and wetter over the vegetation and correspondingly an obvious local circulation in the lower atmosphere is formed. Simulating results also show that maximum updraft and downdraft occur around the vegetation-desert marginal area,where the dynamical and thermodynamical properties of PBL (Planetary Boundary Layer) are uncontinuous.It is stronger at daytime,weaker and reverse at nighttime.In the simulation,the moisture inversion phenomena are analyzed.Finally.the influences of vegetation cover factor exchange on local boundary layer climate are simulated.The simulating results bring to light that water may be conserved and improved by developing tree planting and afforestation,and improving cover factor of vegetation in local ecoenvironment,and this is an important way of transforming local climate in arid and semi-arid area.Results indicate that the coupled model can be used to study the soil-vegetation-atmosphere interaction and local boundary layer climate.展开更多
Atmospheric particulate matter(PM2.5) seriously influences air quality. It is considered one of the main environmental triggers for lung and heart diseases. Air pollutants can be adsorbed by forest. In this study we i...Atmospheric particulate matter(PM2.5) seriously influences air quality. It is considered one of the main environmental triggers for lung and heart diseases. Air pollutants can be adsorbed by forest. In this study we investigated the effect of forest cover on urban PM2.5 concentrations in 12 cities in Heilongjiang Province,China. The forest cover in each city was constant throughout the study period. The average daily concentration of PM2.5 in 12 cities was below 75 lg/m^3 during the non-heating period but exceeded this level during heating period. Furthermore, there were more moderate pollution days in six cities. This indicated that forests had the ability to reduce the concentration of PM2.5 but the main cause of air pollution was excessive human interference and artificial heating in winter. We classified the 12 cities according to the average PM2.5 concentrations. The relationship between PM2.5 concentrations and forest cover was obtained by integrating forest cover, land area,heated areas and number of vehicles in cities. Finally,considering the complexity of PM2.5 formation and based on the theory of random forestry, we selected six cities and analyzed their meteorological and air pollutant data. The main factors affecting PM2.5 concentrations were PM10,NO_2, CO and SO_2 in air pollutants while meteorological factors were secondary.展开更多
The Qinghai Province, situated in the northwest of China, is experiencing a continuous warming which is approximately three times more than the rate of global warming. This ongoing warming has a direct connection to v...The Qinghai Province, situated in the northwest of China, is experiencing a continuous warming which is approximately three times more than the rate of global warming. This ongoing warming has a direct connection to vegetation cover, with significant societal and economic impacts in this region. In the present study, we investigate the correlation between climate change and vegetation cover in Qinghai Province. Analysis shows that in the Qinghai Province, order of NDVI is highest in summer followed by autumn, spring and winter. By calculating the average annual and seasonal-NDVI values, it is deduced that the main type of vegetation cover in the Qinghai Province has an upward trend at the rate of 0.013/10a, 0.016/10a, 0.035/10a and 0.058/10a for annual, winter, spring and summer, respectively. While a downward trend at a rate of 0.056/10a is present in autumn-NDVI. At the 0.01% significance level, a significant positive relationship of winter-NDVI with mean winter precipitation and temperature is revealed. Mean NDVI of spring and autumn show a significant positive relationship with respective seasonal mean precipitation. However, a significant difference is present between mean summer-NDVI and mean summer precipitation. Furthermore, mean NDVI of summer and autumn has a significant negative relationship with respective seasonal mean temperature.展开更多
Taking Lancang County as a study area with a large area of eucalyptus introduction in Yunnan, spatiotemporal change characteristics of vegetation cover, as well as the relationships between Enhanced Vegetation Index（...Taking Lancang County as a study area with a large area of eucalyptus introduction in Yunnan, spatiotemporal change characteristics of vegetation cover, as well as the relationships between Enhanced Vegetation Index（EVl） and climatic factors （temperature and precipitation） were analyzed by using the data of MODIS-EVI from 2005 to 2010. The results indicated that： （1） The vegetation cover was overall good, and the annual average values of EVl were greater than 0.395 and showed a slow increasing trend from 2005 to 2010 in study area; the monthly average values of EVl ranged from 0.296 to 0.538, and seasonal variability was obvious. Monthly average values of EVl usually fell to the lowest level in February and March, and reached the peak in July and August. From the perspective of space, average EVl over the years significantly varied in different towns of Lancang County. During 2005 -2010, in 92.534% area of total, vegetation coverage change were not obvious; in 7.25% area of total, vegeta- tion becoming better; only in 0.02% area of total, vegetation cover were getting worse. （2） Monthly average values of EVl were significantly correlated with monthly average rainfall in Lancang County. The maxima of monthly average EVI and rainfall appeared in August on summer, while the minima of monthly average EVl and rainfall appeared in February and January on winter respectively. （3） Monthly average EVl was somewhat relative with monthly average temperature. The maxima of monthly average EVl and temperature appeared in June and August respectively, while the minima appeared in January and February respectively.展开更多
Anthropogenic activities have altered land cover in Lake Baringo Catchment contributing to increased erosion and sediment transport into water bodies. The study aims at analyzing the spatial and temporal Land Use and ...Anthropogenic activities have altered land cover in Lake Baringo Catchment contributing to increased erosion and sediment transport into water bodies. The study aims at analyzing the spatial and temporal Land Use and Land Cover Changes (LULCC) changes from 1988 to 2018 and to identify the main driving forces. GIS and Remote Sensing techniques, interviews and field observations were used to analyze the changes and drivers of LULCC from 1988-2018. The satellite imagery was selected from SPOT Image for the years 1988, 1998, 2008 and 2018. Environment for Visualizing Images (ENVI 5.3) was used to perform image analysis and classification. The catchment was classified into six major LULC classes which are water bodies, settlement, rangeland, vegetation, farmland and bare land. The results revealed that, between the years 1988-1998, and 1998-2008, water bodies decreased by 2.77% and 0.76% respectively. However, during the years 2008-2018, water body coverage increased by 1.87%. Forest cover steadily increased from 1988-2018. From 1988-1998, 1998-2008 and 2008-2018, farmland was increased by 21.11%, 3.21% and 1.7% while rangeland decreased continuously between the years 1988-1998, 1998-2008 and 2008-2018 in the order 15.14%, 4.13% and 3.74% respectively. Similarly, bare land also reduced by 1.75%, 1.04% and 0.99% between the years 1988-1998, 1998-2008 and 2008-2018 respectively. The findings attributed LULCC to rapid population growth, deforestation, poor farming practices and overstocking. The results will provide valuable information to the relevant stakeholders to formulate evidence-based land use management strategies in order to achieve ecological integrity.展开更多
[Objective] The research aimed to study climatic variation characteristics of snow cover days and its influence factors in Suzhou of Anhui Province during recent 50 years. [Method] According to annual snow cover days ...[Objective] The research aimed to study climatic variation characteristics of snow cover days and its influence factors in Suzhou of Anhui Province during recent 50 years. [Method] According to annual snow cover days and correlated data in Suzhou during 1961-2010, by using linear trend method, accumulative anomaly and complete correlation coefficient method, etc., the climatic variation characteristics of snow cover days and its influence factors in Suzhou were analyzed. [Result] In recent 50 years, the snow cover period in Suzhou presented shortened trend. Except days of snow cover (≥20 cm), the annual snow cover days at each thickness all showed varying degrees of decrease trend. The annual snow cover days had wavy decline trend, and the decline amplitude was 0.84 d/10 a. From the 1960s to prior period of the 1970s, the annual snow cover days presented increase trend. From middle and later periods of the 1970s to middle period of the 1980s, the snow cover days was less and gradually increased from later period of the 1980s to the early 1990s. From middle period of the 1990s to 2003, it entered into less snow period again. From 2004 to now, it presented oscillation of snowy and less-snow alternating. The main climatic factor which affected annual snow cover days in Suzhou was average temperature. The second one was average surface temperature. [Conclusion] The research provided theoretical basis for analyzing climate variation in Suzhou under the background of global climate warming.展开更多
致灾环境因子是滑坡易发性预测建模的输入变量,是指影响滑坡发生、发展和分布的各种边坡自然属性因子。类型齐全且意义明确的致灾环境因子,对提高滑坡易发性结果的准确性和可靠性至关重要。为了进一步明确致灾环境因子的研究现状和未来...致灾环境因子是滑坡易发性预测建模的输入变量,是指影响滑坡发生、发展和分布的各种边坡自然属性因子。类型齐全且意义明确的致灾环境因子,对提高滑坡易发性结果的准确性和可靠性至关重要。为了进一步明确致灾环境因子的研究现状和未来展望,本研究在Web of Science的核心合集数据库中进行了文献检索,标题中包含“landslide susceptibility”,出版日期范围从20130101-20231231,收集了767篇滑坡易发性英文论文构成文献数据库。首先统计每篇文献中致灾环境因子数量、获取方法、来源、重要性和认可度等信息,然后详述了致灾环境因子的定义和物理意义;之后对致灾环境因子的优化选取/组合方法、因子联接方法、因子误差及其适宜性等特征进行了讨论,为后续预测滑坡易发性时选取致灾环境因子的不确定性研究提供参考。综述结果表明:(1)文献数据库中共统计出82种致灾环境因子,使用频率较高的因子有40余种,其中坡度、坡向、高程、岩性是使用频率最高的4个因子,坡度、高程、公路密度、岩性、降雨等因子在滑坡易发性预测中的重要性依次增高;(2)发现采用类型齐全且物理意义明确的致灾环境因子、基于环境因子联接方法来构建模型输入变量、消除环境因子中的随机误差、提升环境因子的适宜性和内在可解释性等研究有利于大幅提升机器学习方法预测滑坡易发性的性能,在未来研究中需要重点关注这些关键问题。展开更多
In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
文摘The Dongsithouane National Production Forest (DNPF) is one of the largest natural forest areas in Savannakhet, Lao PDR, which has been a vital support for the local community’s livelihood, Recently, significant changes in land use and land cover (LULC) have been observed in this area, leading to a reduction of natural forests. There were two separate methods of this study: firstly, to identify LULC changes across three different periods, spectral imagery from the Landsat 5 Thematic Mapper (TM) for the years 2001 and 2011, and the Landsat 8 Operational Land Imager (OLI) for 2021 were used as the primary data sources. The satellite images were preprocessed for various forest classes, including pretreatment of the top of atmosphere reflectance by using QGIS software’s semi-automatic classification plug-in (SCP), and ArcGIS was used for post-classification. A supervised classification approach was applied to the satellite images from 2001, 2011, and 2021 to generate diverse maps of LULC. Secondly, a household survey dataset was used to investigate influential factors. Approximately 220 households were interviewed in order to collect socio-economic information (including data on population growth, increased business activities, location of the area, agriculture land expansion, and need for settlement land). Household survey data was analyzed by using SPSS. Descriptive statistics, including frequency distributions and percentages, were applied to observe characteristics. Additionally, a binary logistic regression model was used to analyze the socioeconomic factors related to LULC change in DNPF. Key findings indicated a decline in natural forest areas within the study site. Specifically, both dry dipterocarp forest (−11.35%) and mixed deciduous forest (−0.18%) decreased from 2001 to 2021. The overall accuracy of the LULC maps was 94%, 86%, and 89% for the years 2001, 2011, and 2021 respectively. In contrast, agricultural land increased significantly by 155.70%, while built-up land, and water bodies increased by 65.54% and 35.33%, respectively. The results also highlighted a significant increase in construction land, up to 65.54%. Furthermore, the study found a correlation between agricultural expansion and a reduction of forest areas, along with an increase in built-up land along the forest areas’ boundaries. Timber exploitation and charcoal production also contributed to the decline in forest cover. The logistic regression model identified significant determinants of LULC change, including the area’s location, agricultural land expansion, increased business activity, and the need for settlement land. These factors have influenced the management of DNPF. Urgent sustainable management practices and actions, including forest ecosystem protection, village agricultural zoning, water source and watershed protection and public awareness, are required to preserve the forest areas of DNPF.
文摘A numerical model has been developed for simulating land-surface processes and atmospheric boundary layer climate of vegetation and desert in semi-arid region.Dynamically,thermal and hydrological processes take place in the atmospheric boundary layer.Vegetation and surface layer of soil are included in the soil-vegetation-atmosphere coupled system,in which,vegetation is considered as a horizontally uniform layer,soil is divided into 13 layers and the horizontal differences of variables in the system are neglected.The influence of local boundary layer climate by vegetation cover factor is simulated with the coupled model in the semi-arid region of Northwest China (around 38°N,105°E).Results indicate that due to significant differences of water and energy budgets in vegetation and desert region,the air is colder and wetter over the vegetation and correspondingly an obvious local circulation in the lower atmosphere is formed. Simulating results also show that maximum updraft and downdraft occur around the vegetation-desert marginal area,where the dynamical and thermodynamical properties of PBL (Planetary Boundary Layer) are uncontinuous.It is stronger at daytime,weaker and reverse at nighttime.In the simulation,the moisture inversion phenomena are analyzed.Finally.the influences of vegetation cover factor exchange on local boundary layer climate are simulated.The simulating results bring to light that water may be conserved and improved by developing tree planting and afforestation,and improving cover factor of vegetation in local ecoenvironment,and this is an important way of transforming local climate in arid and semi-arid area.Results indicate that the coupled model can be used to study the soil-vegetation-atmosphere interaction and local boundary layer climate.
基金supported by the Natural Science Foundation of Heilongjiang Province,China(Grant No.G2016001)
文摘Atmospheric particulate matter(PM2.5) seriously influences air quality. It is considered one of the main environmental triggers for lung and heart diseases. Air pollutants can be adsorbed by forest. In this study we investigated the effect of forest cover on urban PM2.5 concentrations in 12 cities in Heilongjiang Province,China. The forest cover in each city was constant throughout the study period. The average daily concentration of PM2.5 in 12 cities was below 75 lg/m^3 during the non-heating period but exceeded this level during heating period. Furthermore, there were more moderate pollution days in six cities. This indicated that forests had the ability to reduce the concentration of PM2.5 but the main cause of air pollution was excessive human interference and artificial heating in winter. We classified the 12 cities according to the average PM2.5 concentrations. The relationship between PM2.5 concentrations and forest cover was obtained by integrating forest cover, land area,heated areas and number of vehicles in cities. Finally,considering the complexity of PM2.5 formation and based on the theory of random forestry, we selected six cities and analyzed their meteorological and air pollutant data. The main factors affecting PM2.5 concentrations were PM10,NO_2, CO and SO_2 in air pollutants while meteorological factors were secondary.
文摘The Qinghai Province, situated in the northwest of China, is experiencing a continuous warming which is approximately three times more than the rate of global warming. This ongoing warming has a direct connection to vegetation cover, with significant societal and economic impacts in this region. In the present study, we investigate the correlation between climate change and vegetation cover in Qinghai Province. Analysis shows that in the Qinghai Province, order of NDVI is highest in summer followed by autumn, spring and winter. By calculating the average annual and seasonal-NDVI values, it is deduced that the main type of vegetation cover in the Qinghai Province has an upward trend at the rate of 0.013/10a, 0.016/10a, 0.035/10a and 0.058/10a for annual, winter, spring and summer, respectively. While a downward trend at a rate of 0.056/10a is present in autumn-NDVI. At the 0.01% significance level, a significant positive relationship of winter-NDVI with mean winter precipitation and temperature is revealed. Mean NDVI of spring and autumn show a significant positive relationship with respective seasonal mean precipitation. However, a significant difference is present between mean summer-NDVI and mean summer precipitation. Furthermore, mean NDVI of summer and autumn has a significant negative relationship with respective seasonal mean temperature.
基金Supported by National Natural Science Fund Item,China(41361020,40961031)
文摘Taking Lancang County as a study area with a large area of eucalyptus introduction in Yunnan, spatiotemporal change characteristics of vegetation cover, as well as the relationships between Enhanced Vegetation Index（EVl） and climatic factors （temperature and precipitation） were analyzed by using the data of MODIS-EVI from 2005 to 2010. The results indicated that： （1） The vegetation cover was overall good, and the annual average values of EVl were greater than 0.395 and showed a slow increasing trend from 2005 to 2010 in study area; the monthly average values of EVl ranged from 0.296 to 0.538, and seasonal variability was obvious. Monthly average values of EVl usually fell to the lowest level in February and March, and reached the peak in July and August. From the perspective of space, average EVl over the years significantly varied in different towns of Lancang County. During 2005 -2010, in 92.534% area of total, vegetation coverage change were not obvious; in 7.25% area of total, vegeta- tion becoming better; only in 0.02% area of total, vegetation cover were getting worse. （2） Monthly average values of EVl were significantly correlated with monthly average rainfall in Lancang County. The maxima of monthly average EVI and rainfall appeared in August on summer, while the minima of monthly average EVl and rainfall appeared in February and January on winter respectively. （3） Monthly average EVl was somewhat relative with monthly average temperature. The maxima of monthly average EVl and temperature appeared in June and August respectively, while the minima appeared in January and February respectively.
文摘Anthropogenic activities have altered land cover in Lake Baringo Catchment contributing to increased erosion and sediment transport into water bodies. The study aims at analyzing the spatial and temporal Land Use and Land Cover Changes (LULCC) changes from 1988 to 2018 and to identify the main driving forces. GIS and Remote Sensing techniques, interviews and field observations were used to analyze the changes and drivers of LULCC from 1988-2018. The satellite imagery was selected from SPOT Image for the years 1988, 1998, 2008 and 2018. Environment for Visualizing Images (ENVI 5.3) was used to perform image analysis and classification. The catchment was classified into six major LULC classes which are water bodies, settlement, rangeland, vegetation, farmland and bare land. The results revealed that, between the years 1988-1998, and 1998-2008, water bodies decreased by 2.77% and 0.76% respectively. However, during the years 2008-2018, water body coverage increased by 1.87%. Forest cover steadily increased from 1988-2018. From 1988-1998, 1998-2008 and 2008-2018, farmland was increased by 21.11%, 3.21% and 1.7% while rangeland decreased continuously between the years 1988-1998, 1998-2008 and 2008-2018 in the order 15.14%, 4.13% and 3.74% respectively. Similarly, bare land also reduced by 1.75%, 1.04% and 0.99% between the years 1988-1998, 1998-2008 and 2008-2018 respectively. The findings attributed LULCC to rapid population growth, deforestation, poor farming practices and overstocking. The results will provide valuable information to the relevant stakeholders to formulate evidence-based land use management strategies in order to achieve ecological integrity.
文摘[Objective] The research aimed to study climatic variation characteristics of snow cover days and its influence factors in Suzhou of Anhui Province during recent 50 years. [Method] According to annual snow cover days and correlated data in Suzhou during 1961-2010, by using linear trend method, accumulative anomaly and complete correlation coefficient method, etc., the climatic variation characteristics of snow cover days and its influence factors in Suzhou were analyzed. [Result] In recent 50 years, the snow cover period in Suzhou presented shortened trend. Except days of snow cover (≥20 cm), the annual snow cover days at each thickness all showed varying degrees of decrease trend. The annual snow cover days had wavy decline trend, and the decline amplitude was 0.84 d/10 a. From the 1960s to prior period of the 1970s, the annual snow cover days presented increase trend. From middle and later periods of the 1970s to middle period of the 1980s, the snow cover days was less and gradually increased from later period of the 1980s to the early 1990s. From middle period of the 1990s to 2003, it entered into less snow period again. From 2004 to now, it presented oscillation of snowy and less-snow alternating. The main climatic factor which affected annual snow cover days in Suzhou was average temperature. The second one was average surface temperature. [Conclusion] The research provided theoretical basis for analyzing climate variation in Suzhou under the background of global climate warming.
文摘致灾环境因子是滑坡易发性预测建模的输入变量,是指影响滑坡发生、发展和分布的各种边坡自然属性因子。类型齐全且意义明确的致灾环境因子,对提高滑坡易发性结果的准确性和可靠性至关重要。为了进一步明确致灾环境因子的研究现状和未来展望,本研究在Web of Science的核心合集数据库中进行了文献检索,标题中包含“landslide susceptibility”,出版日期范围从20130101-20231231,收集了767篇滑坡易发性英文论文构成文献数据库。首先统计每篇文献中致灾环境因子数量、获取方法、来源、重要性和认可度等信息,然后详述了致灾环境因子的定义和物理意义;之后对致灾环境因子的优化选取/组合方法、因子联接方法、因子误差及其适宜性等特征进行了讨论,为后续预测滑坡易发性时选取致灾环境因子的不确定性研究提供参考。综述结果表明:(1)文献数据库中共统计出82种致灾环境因子,使用频率较高的因子有40余种,其中坡度、坡向、高程、岩性是使用频率最高的4个因子,坡度、高程、公路密度、岩性、降雨等因子在滑坡易发性预测中的重要性依次增高;(2)发现采用类型齐全且物理意义明确的致灾环境因子、基于环境因子联接方法来构建模型输入变量、消除环境因子中的随机误差、提升环境因子的适宜性和内在可解释性等研究有利于大幅提升机器学习方法预测滑坡易发性的性能,在未来研究中需要重点关注这些关键问题。
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
