Some factorizations of graphs into C5-Factors and 1-Factors

In [1], we show that K_{10n} can be factored into \alpha C_5-factors and \beta 1-factors for all non-negative integers \alpha and \beta satisfying 2\alpha + \beta = 10n-1. The constructions in [1] rely on the existence of factorizations of certain graphs into C_5-factors and 1-factors. In this research report we present the necessary factorizations, which were found computationally.

This is joint work by Peter Adams and Darryn Bryant (The University of Queensland), Saad El-Zanati (Illinois State University) and Heather Gavlas (University of Vermont).

[1] Peter Adams, Darryn E. Bryant, Saad I. El-Zanati and Heather Gavlas, Factorizations of the Complete Graph into C_5-Factors and 1-Factors, (submitted).

Here is a copy of the research report, in three formats. For a description and summary of the results, and a short list of references, please use one of these links.