A rainbow blow-up lemma for almost optimally bounded edge-colourings
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 Koml\'os, S\'ark\"ozy and Szemer\'edi that applies to almost optimally bounded colourings. A corollary of this is that there exists a...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
23 Jul 2019
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| In: |
Arxiv
Year: 2019, Pages: 1-28 |
| DOI: | 10.48550/arXiv.1907.09950 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.1907.09950 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1907.09950 
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| Author Notes: | Stefan Ehard, Stefan Glock, and Felix Joos |
| Summary: | 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 Koml\'os, S\'ark\"ozy and Szemer\'edi 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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| Item Description: | Gesehen am 27.07.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.1907.09950 |