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

Fingerprint

Forbidden Subgraph
Hamiltonians
Connected graph
Claw
Degree Sum
Cycle
Path
Induced Subgraph
Isomorphic
Subset
Theorem

Keywords

  • Forbidden subgraphs cycle

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Forbidden subgraphs and the existence of paths and cycles passing through specified vertices. / Fujisawa, Jun; Ota, Katsuhiro; Sugiyama, Takeshi; Tsugaki, Masao.

In: Discrete Mathematics, Vol. 308, No. 24, 28.12.2008, p. 6111-6114.

Research output: Contribution to journalArticle

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