无爪图过特殊子图的路

Paths Through Particular Subgraphs of Claw-Free Graphs

设Ｇ是ｋ—连通无不科，Ｓ是Ｇ的子图．Ｇ中过Ｓ所有顶点的路称为Ｓ—路．证明了：若ａ３（Ｓ）≤ｋ＋１，则Ｇ含Ｓ—路，这里ａ３（Ｓ）为Ｓ的在Ｇ中两两距离至少为３的顶点的最大数目．推广了如下结论；若ａ（Ｇ２）≤ｋ＋１，则Ｇ是可迹的，这里Ｇ２为Ｇ的平方图．

Let G be a k-connected claw-free graph, and S a subgraph of G. A path in G is called an S-path if it contains all venices of S. In this paper, it is proved that G has an S -path if a3 (S)≤k + l, where a3 (S) denotes the maximum number of venices of S that are pairwise at distance at least three in G. The result that G is traceable if a(G2)≤k+l was extended. Where Gi is the square of G.