A factorization theorem for a certain class of graphs

Abstract

In this note we give a necessary and sufficient condition for factorization of graphs satisfying the “odd cycle property”. We show that a graph G with the odd cycle property contains a [ k i ] factor if and only if the sequence [ H]+[ k i ] is graphical for all subgraphs H of the complement of G. A similar theorem is shown to be true for all digraphs.