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

Jun Fujisawa, Atsuhiro Nakamoto, Kenta Ozeki

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)46-60
ページ数15
ジャーナルJournal of Combinatorial Theory. Series B
103
1
DOI
出版ステータスPublished - 2013 1

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学
  • 計算理論と計算数学

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