Longest cycles in 4-connected graphs |
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Authors: | Junqing Cai Hao Li Qiang Sun |
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Institution: | 1. School of Management, Qufu Normal University, Rizhao, PR China;2. LRI, UMR 6823 CNRS and Université Paris-Saclay, B.650, Orsay Cedex, France;3. Institute for Interdisciplinary Research, Jianghan University, Wuhan, PR China;4. School of Mathematical Science, Yangzhou University, Yangzhou, PR China |
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Abstract: | Let is an independent set of a graph G. In this paper, we give a low bound for the length of a longest cycle in a 4-connected graph and get the following result: If is a 4-connected graph on vertices, then the circumference . Moreover, we give graphs to show that the connectivity in our result is best possible with respect to the low bound and the low bound in our result is also best possible with respect to the connectivity. |
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Keywords: | Circumference Non-insertible vertex Independent set |
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