# 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} }

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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