图G的整数k-匹配是由E(G)到{ 0,1,⋯,k }上的映射f,满足对任意点u,所有f(e)的加和不超过k,其中f(e)之和为所有以点u为端点的边e。当k=1时,整数k-匹配即为匹配。(强)整数k-匹配排除数由mpk(G)(smpk(G))表示,是被一个图删去后该图既不存在...图G的整数k-匹配是由E(G)到{ 0,1,⋯,k }上的映射f,满足对任意点u,所有f(e)的加和不超过k,其中f(e)之和为所有以点u为端点的边e。当k=1时,整数k-匹配即为匹配。(强)整数k-匹配排除数由mpk(G)(smpk(G))表示,是被一个图删去后该图既不存在完美整数k-匹配,也不存在几乎完美整数k-匹配的最小点集(点集与边集)的元素数。Caibing Chang、Xianfu Li and Yan Liu介绍了smpk(TQn)。本文提出超强整数k-匹配的定义并证明TQn是超强整数k-匹配图。An integer k-matching of a graph Gis a function ffrom E(G)to { 0,1,⋯,k }such that the sum of f(e)is not more than kfor any vertex u, where the sum of f(e)is taken over all edges eincident to u. When k=1, the integer k-matching is a matching. The (strong) integer k-matching preclusion number, denoted by mpk(G)(smpk(G)), is the number of elements of the minimum vertex (vertices and edges) whose deletion results in a graph with neither perfect integer k-matching nor almost perfect integer k-matching. The smpk(TQn)was introduced by Caibing Chang, Xianfu Li and Yan Liu. In this paper, we denote the super strong integer k-matching and prove that TQnis super strong integer k-matching graph.展开更多
文摘图G的整数k-匹配是由E(G)到{ 0,1,⋯,k }上的映射f,满足对任意点u,所有f(e)的加和不超过k,其中f(e)之和为所有以点u为端点的边e。当k=1时,整数k-匹配即为匹配。(强)整数k-匹配排除数由mpk(G)(smpk(G))表示,是被一个图删去后该图既不存在完美整数k-匹配,也不存在几乎完美整数k-匹配的最小点集(点集与边集)的元素数。Caibing Chang、Xianfu Li and Yan Liu介绍了smpk(TQn)。本文提出超强整数k-匹配的定义并证明TQn是超强整数k-匹配图。An integer k-matching of a graph Gis a function ffrom E(G)to { 0,1,⋯,k }such that the sum of f(e)is not more than kfor any vertex u, where the sum of f(e)is taken over all edges eincident to u. When k=1, the integer k-matching is a matching. The (strong) integer k-matching preclusion number, denoted by mpk(G)(smpk(G)), is the number of elements of the minimum vertex (vertices and edges) whose deletion results in a graph with neither perfect integer k-matching nor almost perfect integer k-matching. The smpk(TQn)was introduced by Caibing Chang, Xianfu Li and Yan Liu. In this paper, we denote the super strong integer k-matching and prove that TQnis super strong integer k-matching graph.
