For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of ...For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of G. In this paper, we prove that if G is a K_(1,4)-free graph of order n and σ_(k+1)(G) ≥ n-k, then p(G) ≤ k, where σ_(k+1)(G) = min{∑v∈S d(v) : S is an independent set of G with |S| = k + 1}.展开更多
The objective of this study was to determine the relationship between PM10 and PM2.5 levels as related to meteorological conditions and traffic flow using both a linear regression analysis and a path analysis. The Par...The objective of this study was to determine the relationship between PM10 and PM2.5 levels as related to meteorological conditions and traffic flow using both a linear regression analysis and a path analysis. The Particulate matter（PM） samples were collected from Sukhumvit road, Bangkok, Thailand, at both open（104 samples） and covered（92 samples）areas along the road. Fifteen percent of all samples were separated before the statistical models were run and used for model validation. The results from the path analysis were more elaborate than those from the linear regression, thus indicating that meteorological conditions had a direct effect on the particulate levels and that the effects of traffic flow were more variable in open areas. The model also indicated that meteorological conditions had an indirect effect and that traffic flow had a direct effect on particulate levels in covered areas. The model validation results indicated that for open areas, the R^2 values were not very different between the path analysis and the linear regression model, but that the path analysis was more accurate than the linear regression model at very low PM concentrations. At high PM concentrations, the path analysis model also had a better fit than did the linear regression, so the predictions from the path analysis model were more accurate than those from the linear regression.展开更多
基金Supported by the Joint Fund of Liaoning Provincial Natural Science Foundation(Grant No.SY2016012)
文摘For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of G. In this paper, we prove that if G is a K_(1,4)-free graph of order n and σ_(k+1)(G) ≥ n-k, then p(G) ≤ k, where σ_(k+1)(G) = min{∑v∈S d(v) : S is an independent set of G with |S| = k + 1}.
文摘The objective of this study was to determine the relationship between PM10 and PM2.5 levels as related to meteorological conditions and traffic flow using both a linear regression analysis and a path analysis. The Particulate matter（PM） samples were collected from Sukhumvit road, Bangkok, Thailand, at both open（104 samples） and covered（92 samples）areas along the road. Fifteen percent of all samples were separated before the statistical models were run and used for model validation. The results from the path analysis were more elaborate than those from the linear regression, thus indicating that meteorological conditions had a direct effect on the particulate levels and that the effects of traffic flow were more variable in open areas. The model also indicated that meteorological conditions had an indirect effect and that traffic flow had a direct effect on particulate levels in covered areas. The model validation results indicated that for open areas, the R^2 values were not very different between the path analysis and the linear regression model, but that the path analysis was more accurate than the linear regression model at very low PM concentrations. At high PM concentrations, the path analysis model also had a better fit than did the linear regression, so the predictions from the path analysis model were more accurate than those from the linear regression.
