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.
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© 2007 Springer Berlin Heidelberg
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Qu, X., Lin, H. (2007). Quasilocally Connected, Almost Locally Connected Or Triangularly Connected Claw-Free Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_17
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DOI: https://doi.org/10.1007/978-3-540-70666-3_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70665-6
Online ISBN: 978-3-540-70666-3
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