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arXiv · 1907.09950

A rainbow blow-up lemma for almost optimally bounded edge-colourings

Stefan Ehard·Stefan Glock·Felix Joos
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Abstract

A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. We prove a rainbow version of the blow-up lemma of Komlós, Sárközy and Szemerédi that applies to almost optimally bounded colourings. A corollary of this is that there exists a rainbow copy of any bounded-degree spanning subgraph $H$ in a quasirandom host graph $G$, assuming that the edge-colouring of $G$ fulfills a boundedness condition that is asymptotically best possible. This has many applications beyond rainbow colourings, for example to graph decompositions, orthogonal double covers and graph labellings.

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Stefan Ehard, Stefan Glock, Felix Joos. 2019-07-23. A rainbow blow-up lemma for almost optimally bounded edge-colourings. https://arxiv.org/abs/1907.09950

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