Monochromatic partitions in 2-edge-coloured bipartite graphs
Combinatorics
2024-03-20 v1
Abstract
We study two variations of the Gyarfas--Lehel conjecture on the minimum number of monochromatic components needed to cover an edge-coloured complete bipartite graph. Specifically, we show the following. - For p>> (\log n/n)^{1/2}, w.h.p.~every 2-colouring of the random bipartite graph G~ G(n,n,p) admits a cover of all but O(1/p) vertices of G using at most three vertex-disjoint monochromatic components. - For every 2-colouring of a bipartite graph G with parts of size n and minimum degree (13/16+o(1))n, the vertices of G can be covered using at most three vertex-disjoint monochromatic components.
Keywords
Cite
@article{arxiv.2403.12587,
title = {Monochromatic partitions in 2-edge-coloured bipartite graphs},
author = {Camila Fernández and Matías Pavez-Signé and Maya Stein},
journal= {arXiv preprint arXiv:2403.12587},
year = {2024}
}