Arc-transitive cycle decompositions of tetravalent graphs

Štefko Miklavič, Primož Potočnik, Stephen E Wilson

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A cycle decomposition of a graph Γ is a set C of cycles of Γ such that every edge of Γ belongs to exactly one cycle in C. Such a decomposition is called arc-transitive if the group of automorphisms of Γ that preserve C setwise acts transitively on the arcs of Γ. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.

Original languageEnglish (US)
Pages (from-to)1181-1192
Number of pages12
JournalJournal of Combinatorial Theory. Series B
Volume98
Issue number6
DOIs
StatePublished - Nov 2008

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Cycle Decomposition
Arc of a curve
Decomposition
Arc-transitive Graph
Graph in graph theory
Cycle
Connected graph
Automorphisms
Isomorphic
Decompose

Keywords

  • Automorphism group
  • Consistent cycle
  • Cycle decomposition
  • Graph
  • Medial maps

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Arc-transitive cycle decompositions of tetravalent graphs. / Miklavič, Štefko; Potočnik, Primož; Wilson, Stephen E.

In: Journal of Combinatorial Theory. Series B, Vol. 98, No. 6, 11.2008, p. 1181-1192.

Research output: Contribution to journalArticle

Miklavič, Štefko ; Potočnik, Primož ; Wilson, Stephen E. / Arc-transitive cycle decompositions of tetravalent graphs. In: Journal of Combinatorial Theory. Series B. 2008 ; Vol. 98, No. 6. pp. 1181-1192.
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