Graphs and digraphs with all 2-factors isomorphic

  • Authors:

  • M. Abreu;R. E. L. Aldred;M. Funk;Bill Jackson;D. Labbate;J. Sheehan

  • Affiliations:

  • Dipartimento di Matematica, Università della Basilicata, I-85100 Potenza, Italy;University of Otago, P. O. Box 56, Dunedin, New Zealand;Dipartimento di Matematica, Università della Basilicata, I-85100 Potenza, Italy;School of Mathematical Sciences, Queen Mary College, London El 4NS, England;Dipartimento di Matematica, Politecnico di Bari, I-70125 Bari, Italy;Department of Mathematical Sciences, King's College, University of Aberdeen, Edward Wright Building, Dunbar Street, Old Aberdeen AB24 3UE, Scotland

  • Venue:
  • Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
  • Year:
  • 2004

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Abstract

We show that a digraph which contains a directed 2-factor and has minimum in-degree and out-degree at least four has two non-isomorphic directed 2-factors. As a corollary, we deduce that every graph which contains a 2-factor and has minimum degree at least eight has two non-isomorphic 2- factors. In addition we construct: an infinite family of 3-diregular digraphs with the property that all their directed 2-factors are Hamilton cycles, an in finite family of 2-connected 4-regular graphs with the property that all their 2-factors are isomorphic, and an infinite family of cyclically 6-edge-connected cubic graphs with the property that all their 2-factors are Hamilton cycles.