Regular Graphs of High Degree are 1-Factorizable.

Chetwynd, Amanda G. and Hilton, A. J. W. (1985) Regular Graphs of High Degree are 1-Factorizable. Proceedings of the London Mathematical Society, Series (2). pp. 193-206. ISSN 1460-244X

Abstract

It is a well-known conjecture that if a regular graph G of order 2n has degree d(G) satisfying d(G) n, then G is the union of edge-disjoint 1-factors. It is well known that this conjecture is true for d(G) equal to 2n—1 or 2n—2. We show here that it is true for d(G) equal to 2n — 3, 2n — 4, or 2n — 5. We also show that it is true for d(G) |V(G)|.