Geodesic
Monochromatic cycle partitions of \(2\)-coloured graphs with minimum degree \(3n/4\)
Shoham Letzter1
1ETH Institute for Theoretical Studies
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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Balogh, Barát, Gerbner, Gyárfás, and Sárközy made 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 this conjecture for large $n$, improving approximate results by the aforementioned authors and by DeBiasio and Nelsen.
DOI : 10.37236/7239
Classification : 05C55, 05C38, 05C70, 05D10
Mots-clés : regularity lemma, absorbing, robust expansion, monochromatic partitioning, Ramsey-type problem

Shoham Letzter  1

1 ETH Institute for Theoretical Studies 
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Shoham Letzter. Monochromatic cycle partitions of \(2\)-coloured graphs with minimum degree \(3n/4\). The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7239

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