Four Blocks Cycles C(k,1,1,1) in Digraphs
Combinatorics
2022-01-10 v1
Abstract
A four blocks cycle C(k1,k2,k3,k4) is an oriented cycle formed by the union of four internally disjoint directed paths of lengths k1,k2,k3 and k4 respectively. El Mniny proved that if D is a digraph having a spanning out-tree T with no subdivisions of C(k, 1, 1, 1), then the chromatic number of D is at most 8^{3}k. In this paper, we will improve this bound to 18k.
Keywords
Cite
@article{arxiv.2201.02520,
title = {Four Blocks Cycles C(k,1,1,1) in Digraphs},
author = {Zahraa Mohsen},
journal= {arXiv preprint arXiv:2201.02520},
year = {2022}
}