Circumferences of regular claw-free graphs |
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| Authors: | MingChu Li |
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| Institution: | a College of Science, Chongqing Technology and Business University, Chongqing 400067, P.R. China
b School of Software, Dalian University of Technology, Dalian, Liaoning 116620, P.R. China |
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| Abstract: | A known result obtained independently by Fan and Jung is that every 3-connected k-regular graph on n vertices contains a cycle of length at least min{3k,n}. This raises the question of how much can be said about the circumferences of 3-connected k-regular claw-free graphs. In this paper, we show that every 3-connected k-regular claw-free graph on n vertices contains a cycle of length at least min{6k-17,n}. |
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| Keywords: | Circumference Longest cycle Claw-free graph Regularity 3-connectedness |
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