Forbidden subgraphs and the existence of paths and cycles passing through specified vertices

Jun Fujisawa, Katsuhiro Ota, Takeshi Sugiyama, Masao Tsugaki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In [H. Broersma, H. Li, J. Li, F. Tian, H.J. Veldman, Cycles through subsets with large degree sums, Discrete Math. 171 (1997) 43-54], Duffus et al. showed that every connected graph G which contains no induced subgraph isomorphic to a claw or a net is traceable. They also showed that if a 2-connected graph G satisfies the above conditions, then G is hamiltonian. In this paper, modifying the conditions of Duffus et al.'s theorems, we give forbidden structures for a specified set of vertices which assures the existence of paths and cycles passing through these vertices.

Original languageEnglish
Pages (from-to)6111-6114
Number of pages4
JournalDiscrete Mathematics
Volume308
Issue number24
DOIs
Publication statusPublished - 2008 Dec 28

Keywords

  • Forbidden subgraphs cycle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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