A rainbow blowup lemma for almost optimally bounded edgecolourings
Abstract
A subgraph of an edgecoloured graph is called rainbow if all its edges have different colours. We prove a rainbow version of the blowup 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 boundeddegree spanning subgraph $H$ in a quasirandom host graph $G$, assuming that the edgecolouring 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2019
 arXiv:
 arXiv:1907.09950
 Bibcode:
 2019arXiv190709950E
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 28 pages