@inproceedings{Ellingham1988IsomorphicFO, title={Isomorphic Factorization of Regular Graphs and 3-regular Multigraphs}, author={Mark N. Ellingham and Nicholas C. Wormald}, year={1988} }

- Published 1988

A multigraph G is divisible by t if its edge set can be partitioned into / subsets, such that the subgraphs (called factors) induced by the subsets are all isomorphic. If G has e(G) edges, then it is t-rational if it is divisible by t or if / does not divide e{G). A short proof is given that any graph G is /-rational for all t ^ x'(G) ( t n e chromatic index of G), and thus any r-regular graph is /-rational for all / ^ r + 1. The main result of this paper is that all 3-regular multigraphs are… CONTINUE READING