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arXiv · 2001.00643

Long monochromatic even cycles in 3-edge-coloured graphs of large minimum degree

Tomasz Łuczak·Zahra Rahimi
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Abstract

We show that for every $η>0$, there exists $n_0$ such that for every even $n$, $n\ge n_0$, and every graph $G$ with $(2+η)n$ vertices and minimum degree at least $(7/4+4η)n$, each colouring of the edges of $G$ with three colours results in a monochromatic cycle of length $n$.

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Tomasz Łuczak, Zahra Rahimi. 2020-01-02. Long monochromatic even cycles in 3-edge-coloured graphs of large minimum degree. https://arxiv.org/abs/2001.00643

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