A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-o-1-heavy if every induced claw(K_(1,3)) of G has a pair of n...A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-o-1-heavy if every induced claw(K_(1,3)) of G has a pair of nonadjacent vertices with degree sum at least n-1 in G. In this paper we show that a claw-o-1-heavy graph G is traceable if we impose certain additional conditions on G involving forbidden induced subgraphs.展开更多
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum o...A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.展开更多
基金Supported by the National Natural Science Foundation of China(No.11601429,11671320 and U1803263)the Fundamental Research Funds for the Central Universities(No.3102018zy035)
文摘A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-o-1-heavy if every induced claw(K_(1,3)) of G has a pair of nonadjacent vertices with degree sum at least n-1 in G. In this paper we show that a claw-o-1-heavy graph G is traceable if we impose certain additional conditions on G involving forbidden induced subgraphs.
基金Supported by the National Natural Science Foundation of China(No.11571135,11601429 and 11671320)the Natural Science Foundation of Shaanxi Province(No.2016JQ1002)
文摘A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.
