ABSTRACT
In this chapter, the authors present an introduction to a psuedo-one-factorizations of regular graphs of odd order I. All graphs the authors deal with are finite and have neither loops nor multiple edges. A graph is called k-regular if all its vertices have the same valency k. Clearly, in order for a graph to have a one-factorization, it is necessary that it is a regular graph of even order. The authors briefly review the clique partitions of a class of graphs, which is equivalent to the pseudo-one-factorizations of graphs. They present several methods of constructing graphs which are either factorizable or not. The authors consider the structure of a pseudo-one-factorization of a graph, and formulate the pseudo-one-factorization conjecture, in particular, they prove that a class of (v -3)-regular graphs of order v are factorizable.
