Journal of the Australian Mathematical Society

Research Article

A theorem on connected graphs in which every edge belongs to a 1-factor

Charles H. C. Littlea1

a1 Department of Mathematics and Computer Science Royal Melbourne Institute of Technology, Victoria, 3000, Australia

In this paper, we consider factor covered graphs, which are defined basically as connected graphs in which every edge belongs to a 1-factor. The main theorem is that for any two edges e and e′ of a factor covered graph, there is a cycle C passing through e and e′ such that the edge set of C is the symmetric difference of two 1-factors.

(Received April 27 1973)