Monochromatic cycle partitions of $2$-coloured graphs with minimum degree $3n/4$

Shoham Letzter

Monochromatic cycle partitions of $2$-coloured graphs with minimum degree $3n/4$

Combinatorics 2015-02-27 v1

Authors: Shoham Letzter

Abstract

Balogh, Bar\'at, Gerbner, Gy\'arf\'as, and S\'ark\"ozy proposed the following conjecture. Let $G$ be a graph on $n$ vertices with minimum degree at least $3n/4$ . Then for every $2$ -edge-colouring of $G$ , the vertex set $V(G)$ may be partitioned into two vertex-disjoint cycles, one of each colour. We prove that this conjecture holds for $n$ large enough, improving approximate results by the aforementioned authors and by DeBiasio and Nelsen.

Keywords

monochromatic cycle partition 2-edge-coloured graph minimum degree Dirac-type conjecture cycle decomposition graph partition

Cite

@article{arxiv.1502.07736,
  title  = {Monochromatic cycle partitions of $2$-coloured graphs with minimum degree $3n/4$},
  author = {Shoham Letzter},
  journal= {arXiv preprint arXiv:1502.07736},
  year   = {2015}
}

Comments

69 pages, 6 figures

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