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
为了在复杂多变的电子战场景下对密集重叠的雷达脉冲信号进行快速准确的分选,稀释脉冲流,解决现有基于密度的空间聚类算法(Density-based Spatial Clustering of Applications with Noise,DBSCAN)在分选时易受干扰点影响、聚类参数需要...为了在复杂多变的电子战场景下对密集重叠的雷达脉冲信号进行快速准确的分选,稀释脉冲流,解决现有基于密度的空间聚类算法(Density-based Spatial Clustering of Applications with Noise,DBSCAN)在分选时易受干扰点影响、聚类参数需要人为设置、算法复杂度高的问题,提出了一种面向雷达信号预分选的粒子群快速密度聚类算法(Particle Swarm Fast Density Clustering Algorithm,PSK-DBSCAN)。该算法首先引入数据场理论剔除雷达脉冲信号里的干扰点,提升了分选准确度;其次,引入粒子群算法并设计了基于轮廓系数的适应度函数,自适应地获得最优聚类参数;最后,使用K-D(K-Dimensional)树降低DBSCAN的算法复杂度,减少分选时间。经实验验证,算法可以对复杂交错的雷达脉冲信号实现快速聚类分选,正确率达到98.9%,性能稳定。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.
文摘为了在复杂多变的电子战场景下对密集重叠的雷达脉冲信号进行快速准确的分选,稀释脉冲流,解决现有基于密度的空间聚类算法(Density-based Spatial Clustering of Applications with Noise,DBSCAN)在分选时易受干扰点影响、聚类参数需要人为设置、算法复杂度高的问题,提出了一种面向雷达信号预分选的粒子群快速密度聚类算法(Particle Swarm Fast Density Clustering Algorithm,PSK-DBSCAN)。该算法首先引入数据场理论剔除雷达脉冲信号里的干扰点,提升了分选准确度;其次,引入粒子群算法并设计了基于轮廓系数的适应度函数,自适应地获得最优聚类参数;最后,使用K-D(K-Dimensional)树降低DBSCAN的算法复杂度,减少分选时间。经实验验证,算法可以对复杂交错的雷达脉冲信号实现快速聚类分选,正确率达到98.9%,性能稳定。
