Cycles with two blocks in k‐chromatic digraphs

@article{Kim2016CyclesWT,
title={Cycles with two blocks in k‐chromatic digraphs},
author={Ringi Kim and Seog-Jin Kim and Jie Ma and Boram Park},
journal={Journal of Graph Theory},
year={2016},
volume={88},
pages={592 - 605}
}
• Published 19 October 2016
• Mathematics
• Journal of Graph Theory
Let k and ℓ be positive integers. A cycle with two blocks c(k,ℓ) is a digraph obtained by an orientation of an undirected cycle, which consists of two internally (vertex) disjoint paths of lengths at least k and ℓ, respectively, from a vertex to another one. A problem of Addario‐Berry, Havet and Thomassé [J. Combin. Theory Ser. B 97 (2007), 620–626] asked if, given positive integers k and ℓ such that k+ℓ≥4 , any strongly connected digraph D containing no c(k,ℓ) has chromatic number at most k…
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