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

Part of: Graph theory Designs and configurations

Published online by Cambridge University Press:  30 October 2020

Stefan Ehard ,
Stefan Glock  and
Felix Joos Open the ORCID record for Felix Joos [Opens in a new window]
Stefan Ehard
Affiliation:
Institut für Optimierung und Operations Research, Universität Ulm, Germany; stefan.ehard@uni-ulm.de
Stefan Glock
Affiliation:
Institute for Theoretical Studies, ETH Zürich, Switzerland; stefan.glock@eth-its.ethz.ch
Felix Joos
Affiliation:
Institut für Informatik, Universität Heidelberg, Germany; joos@informatik.uni-heidelberg.de

Abstract

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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.

Keywords

blow-up lemmarainbow colourings

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs
Secondary: 05C35: Extremal problems 05C51: Graph designs and isomomorphic decomposition 05C60: Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C70: Factorization, matching, partitioning, covering and packing 05C78: Graph labelling (graceful graphs, bandwidth, etc.) 05B40: Packing and covering
Type
Discrete Mathematics
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e37
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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