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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Quasilocally Connected, Almost Locally Connected Or Triangularly Connected Claw-Free Graphs
verfasst von : Xiaoying Qu, Houyuan Lin
Erschienen in: Discrete Geometry, Combinatorics and Graph Theory
Verlag: Springer Berlin Heidelberg
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The definitions of quasilocally connected graphs, almost locally connected graphs and triangularly connected graphs are introduced by Zhang, Teng and Lai et al. They are all different extensions of locally connected graphs. Many known results on the condition of local connectivity have been extended to these weaker conditions mentioned above. In this paper, we study the relations among these different conditions. In particular, we prove that every triangularly connected claw-free graph without isolated vertices is also quasilocally connected claw-free.