The anti-Oberwolfach solution: pancyclic 2-factorizations of complete graphs

Authors:
Brett Stevens
Affiliations:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
Venue:
Theoretical Computer Science - Latin American theoretical informatics
Year:
2003

Citing 4
Cited 0

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Abstract

We pose and completely solve the existence of pancyclic 2-factorizations of complete graphs and complete bipartite graphs. Such 2-factorizations exist for all such graphs, except a few small cases which we have proved are impossible. The solution method is simple but powerful. The pancyclic problem is intended to showcase the power this method offers to solve a wide range of 2-factorization problems. Indeed, these methods go a long way towards being able to produce arbitrary 2-factorizations with one or two cycles per factor.