Four Blocks Cycles C(k,1,1,1) in Digraphs

2022/01/07 by Mohsen, Zahraa
#05C15 #05C20 #05C38 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.02520

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 8³k. In this paper, we will improve this bound to 18k.

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