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arXiv · 2511.12505

Rainbow subgraphs of star-coloured graphs

Allan Lo·Klas Markström·Dhruv Mubayi·Katherine Staden·Maya Stein·Lea Weber
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Abstract

An edge-colouring of a graph $G$ can fail to be rainbow for two reasons: either it contains a monochromatic cherry (a pair of incident edges), or a monochromatic matching of size two. A colouring is a proper colouring if it forbids the first structure, and a star-colouring if it forbids the second structure. In this paper, we study rainbow subgraphs in star-coloured graphs and determine the maximum number of colours in a star-colouring of a large complete graph which does not contain a rainbow copy of a given graph $H$. This problem is a special case of one studied by Axenovich and Iverson on generalised Ramsey numbers and we extend their results in this case.

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Allan Lo, Klas Markström, Dhruv Mubayi, Katherine Staden, Maya Stein, Lea Weber. 2025-11-16. Rainbow subgraphs of star-coloured graphs. https://arxiv.org/abs/2511.12505

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