Perfect 1-Factorisations of Circulants with Small Degree (original) (raw)

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Keywords: one-factorisation, perfect one-factorisation, circulant graph

Abstract

A 111-factorisation of a graph GGG is a decomposition of GGG into edge-disjoint 111-factors (perfect matchings), and a perfect 111-factorisation is a 111-factorisation in which the union of any two of the 111-factors is a Hamilton cycle. We consider the problem of the existence of perfect 111-factorisations of even order circulant graphs with small degree. In particular, we characterise the 333-regular circulant graphs that admit a perfect 111-factorisation and we solve the existence problem for a large family of 444-regular circulants. Results of computer searches for perfect 111-factorisations of 444-regular circulant graphs of orders up to 303030 are provided and some problems are posed.

Author Biographies

Sarada Herke, The University of Queensland

PhD student, School of Mathematics and Physics

Barbara Maenhaut, The University of Queensland

Lecturer, School of Mathematics and Physics

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How to Cite

Herke, S., & Maenhaut, B. (2013). Perfect 1-Factorisations of Circulants with Small Degree. The Electronic Journal of Combinatorics, 20(1), #P58. https://doi.org/10.37236/2264