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arXiv · 2609.17567

Exact three-component covers in 2-coloured random bipartite graphs

Xiao-Chuan Liu·Xu Yang
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Abstract

We resolve the two-colour three-component conjecture of Fernández, Pavez-Signé and Stein for random bipartite graphs. More precisely, we prove that if $G\sim G(n,n,p)$ and $p\gg\sqrt{\log n/n}$, then with high probability every red--blue edge-colouring of $G$ admits a cover of its vertex set by at most three monochromatic connected components. The proof is based on a uniform expansion lemma for unions of common neighbourhoods and an alternating common-neighbourhood expansion argument.

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Xiao-Chuan Liu, Xu Yang. 2026-07-25. Exact three-component covers in 2-coloured random bipartite graphs. https://arxiv.org/abs/2609.17567

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