Quasilocally connected, almost locally connected Or triangularly connected claw-free graphs

Authors:
Xiaoying Qu;Houyuan Lin
Affiliations:
Center for Combinatorics, LPMC, Nankai University, Tianjin, P.R. China;School of Statistics and Mathematics Sciences, Shandong Economic University, Jinan, P.R. China
Venue:
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Year:
2005

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Abstract

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.