Cycles with consecutive odd lengths
Combinatorics
2014-10-03 v1
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.
Cite
@article{arxiv.1410.0430,
title = {Cycles with consecutive odd lengths},
author = {Jie Ma},
journal= {arXiv preprint arXiv:1410.0430},
year = {2014}
}
Comments
7 pages