1-Factorizing Regular Graphs of High Degree-an Improved Bound

Chetwynd, A. G. and Hilton, A. J.W. (1989) 1-Factorizing Regular Graphs of High Degree-an Improved Bound. Annals of Discrete Mathematics, 43 (C). pp. 103-112. ISSN 0167-5060

Abstract

We showed eariler that a regular simple graph of even order satisfying d(G) » 6/7|V(G)| was the union of edge-disjoint 1-factors. Here we improve this to regular simple graphs of even order satisfying d(G)≥ 1/2(√7- 1)|V(G)|.