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 Komlós, Sárközy, and Szemerédi that applies to almost optimally bounded colourings. A corollary of this is that there exists a rainbow copy of any bo...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
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30 October 2020
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| In: |
Forum of mathematics. Sigma
Year: 2020, Jahrgang: 8, Pages: 1-32 |
| ISSN: | 2050-5094 |
| DOI: | 10.1017/fms.2020.38 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1017/fms.2020.38 Verlag, lizenzpflichtig, Volltext: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/rainbow-blowup-lemma-for-almost-optimally-bounded-edgecolourings/9C0AE7E446B2C742A920DB164A04412F 
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| Verfasserangaben: | Stefan Ehard, Stefan Glock and Felix Joos |
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| 520 | |a 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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