Rainbow subgraphs of star-coloured graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917084093480960 |
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| author | Lo, Allan Markström, Klas Mubayi, Dhruv Staden, Katherine Stein, Maya Weber, Lea |
| author_facet | Lo, Allan Markström, Klas Mubayi, Dhruv Staden, Katherine Stein, Maya Weber, Lea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rainbow subgraphs of star-coloured graphs Lo, Allan Markström, Klas Mubayi, Dhruv Staden, Katherine Stein, Maya Weber, Lea Combinatorics 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. |
| title | Rainbow subgraphs of star-coloured graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.12505 |