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arXiv · 1410.0430

Cycles with consecutive odd lengths

Jie Ma
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Abstract

It is proved that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence of the absolute constant d > 0 that every non-bipartite 2-connected graph with minimum degree at least dk contains cycles of all lengths modulo k, thus providing an answer (in a strong form) to a question of Thomassen. Both results are sharp up to the constant factors.

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Jie Ma. 2014-10-02. Cycles with consecutive odd lengths. https://arxiv.org/abs/1410.0430

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