Proof of the 1-Factorization and Hamilton Decomposition Conjectures

@inproceedings{Csaba2013ProofOT,
title={Proof of the 1-Factorization and Hamilton Decomposition Conjectures},
author={B{\'e}la Csaba and Daniela K{\"u}hn and Allan Lo and Deryk Osthus and Andrew Treglown},
year={2013}
}

In this paper we prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D ≥ 2 n/4 − 1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G) = D. (ii) [Hamilton decomposition conjecture] Suppose thatD ≥ n/2 . Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of… CONTINUE READING