Cycles with consecutive odd lengths
نویسنده
چکیده
In this paper we prove 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 in [14]. Both results are sharp up to the constant factors.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 52 شماره
صفحات -
تاریخ انتشار 2016