Hamiltonian cycles in bipartite toroidal graphs with a partite set of degree four vertices

Jun Fujisawa, Atsuhiro Nakamoto, Kenta Ozeki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let G be a 3-connected bipartite graph with partite sets X ∪ Y which is embeddable in the torus. We shall prove that G has a Hamiltonian cycle if (i) G is balanced, i.e., |X| = |Y|, and (ii) each vertex x∈ X has degree four. In order to prove the result, we establish a result on orientations of quadrangular torus maps possibly with multiple edges. This result implies that every 4-connected toroidal graph with toughness exactly one is Hamiltonian, and partially solves a well-known Nash-Williams' conjecture.

Original languageEnglish
Pages (from-to)46-60
Number of pages15
JournalJournal of Combinatorial Theory. Series B
Volume103
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Keywords

  • Bipartite graph
  • Hamiltonian cycle
  • Quadrangulation
  • Torus

ASJC Scopus subject areas

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

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