Bispindles in strongly connected digraphs with large chromatic number
Abstract
A $(k_1+k_2)$bispindle is the union of $k_1$ $(x,y)$dipaths and $k_2$ $(y,x)$dipaths, all these dipaths being pairwise internally disjoint. Recently, Cohen et al. showed that for every $(1,1)$ bispindle $B$, there exists an integer $k$ such that every strongly connected digraph with chromatic number greater than $k$ contains a subdivision of $B$. We investigate generalisations of this result by first showing constructions of strongly connected digraphs with large chromatic number without any $(3,0)$bispindle or $(2,2)$bispindle. Then we show that strongly connected digraphs with large chromatic number contains a $(2,1)$bispindle, where at least one of the $(x,y)$dipaths and the $(y,x)$dipath are long.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.02230
 Bibcode:
 2017arXiv170302230C
 Keywords:

 Mathematics  Combinatorics