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arXiv · 2607.21915

On monochromatic path covers conjecture of Erdős--Gyárfás

Hangdi Chen·Yaojun Chen
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Abstract

Erdős and Gyárfás conjectured in 1995 that, in every red--blue edge-coloring of a complete graph $K_n$, the vertex set can be covered by at most $\sqrt n$ monochromatic paths, all of the same color. Pokrovskiy, Versteegen and Williams (JCT-B, 2026) proved the conjecture for all sufficiently large $n$. In this paper, by using minimal counterexample method, we confirm the conjecture completely.

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Hangdi Chen, Yaojun Chen. 2026-07-24. On monochromatic path covers conjecture of Erdős--Gyárfás. https://arxiv.org/abs/2607.21915

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