A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and numb...A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if for any cut-set , then G has a k-tree.展开更多
Abstract The paper proves that if G is a k tree, then the bandwidth B(G) of the complement G of G is given by B(G)=n-k-1, when GK k+K n-k , n-k-2, otherwise.
A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote ...A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.展开更多
针对目前城市道路场景中行道树提取方法需要设置的参数较多以及树冠点云相互重叠难以精确分割的问题,文章采用一种行道树提取与单株木分割算法。首先通过布料滤波算法从原始点云中移除地面点,并利用半径滤波滤除离群点,去除地面点和噪...针对目前城市道路场景中行道树提取方法需要设置的参数较多以及树冠点云相互重叠难以精确分割的问题,文章采用一种行道树提取与单株木分割算法。首先通过布料滤波算法从原始点云中移除地面点,并利用半径滤波滤除离群点,去除地面点和噪声点对行道树提取的影响;然后通过增加PointNet++网络的点集抽象模块(set abstraction,SA)提高模型特征提取能力,使模型更适用于行道树点云的提取,并利用改进后的网络从原始点云中提取行道树点云;最后结合密度聚类算法(density-based spatial clustering of applications with noise,DBSCAN)与K-Means算法对相互重叠的行道树点云进行分割,得到单株木信息。为验证该方法的有效性,以北京永昌路道路数据集进行训练测试。结果表明:改进后模型的行道树点云平均提取精度和交并比(intersection over union,IoU)分别提高了9.2%和15.1%,达到了94.5%、0.916;单木分割平均精度达到了91.3%。展开更多
文摘A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if for any cut-set , then G has a k-tree.
文摘Abstract The paper proves that if G is a k tree, then the bandwidth B(G) of the complement G of G is given by B(G)=n-k-1, when GK k+K n-k , n-k-2, otherwise.
基金Partially supported by National Natural Science Foundation of China(No.11771172)key scientific and technological project of higher education of Henan Province(No.19A110019)+1 种基金Science and technology innovation fund of Henan Agricultural University(No.KJCX2019A15)Partially supported by the Ph D Research Foundation of Henan Agricultural University(No.30500614)
文摘A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.
文摘针对目前城市道路场景中行道树提取方法需要设置的参数较多以及树冠点云相互重叠难以精确分割的问题,文章采用一种行道树提取与单株木分割算法。首先通过布料滤波算法从原始点云中移除地面点,并利用半径滤波滤除离群点,去除地面点和噪声点对行道树提取的影响;然后通过增加PointNet++网络的点集抽象模块(set abstraction,SA)提高模型特征提取能力,使模型更适用于行道树点云的提取,并利用改进后的网络从原始点云中提取行道树点云;最后结合密度聚类算法(density-based spatial clustering of applications with noise,DBSCAN)与K-Means算法对相互重叠的行道树点云进行分割,得到单株木信息。为验证该方法的有效性,以北京永昌路道路数据集进行训练测试。结果表明:改进后模型的行道树点云平均提取精度和交并比(intersection over union,IoU)分别提高了9.2%和15.1%,达到了94.5%、0.916;单木分割平均精度达到了91.3%。
