On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture
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Date
2021-05-01
Authors
Hompe, Patrick
Pelikánová, Petra
Pokorná, Aneta
Spirkl, Sophie
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
For a digraph G and v is an element of V(G), let delta(+)(v) be the number of out-neighbors of v in G. The Caccetta-Haggkvist conjecture states that for all k >= 1, if G is a digraph with n = |V(G)| such that delta(+)(v) >= k for all v is an element of V(G), then G contains a directed cycle of length at most [n/k]. In Aharoni et al. (2019), Aharoni proposes a generalization of this conjecture, that a simple edge-colored graph on n vertices with n color classes, each of size k, has a rainbow cycle of length at most.n/k.. In this paper, we prove this conjecture if each color class has size Omega(k log k).
Description
The final publication is available at Elsevier via https://doi.org/10.1016/j.disc.2021.112319. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
directed graph, rainbow, Caccetta–Haggkvist conjecture, directed cycle