Speaker:

David Cariolaro (University of Reading, U.K. )

Title:

The 1-factorization conjecture and other edge-coloring problems

Abstract:

A 1-factor in a graph G is a 1-regular spanning subgraph. A 1-factorization of G is a decomposition of G into edge-disjoint 1-factors. The 1-factorization conjecture claims that every D-regular graph of order 2N is 1-factorizable if D greater than or equal to N. It is so far proven only in some particular case. In this talk we shall discuss the 1-factorization conjecture, emphasizing connections with other related edge-coloring problems.