Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices

Takeshi Sugiyama; Masao Tsugaki

ArticleOriginal scientific text

Title

Pairs of forbidden class of subgraphs concerning $K_{1, 3}$ and P₆ to have a cycle containing specified vertices

Authors ¹, ²

Affiliations

Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Abstract

In [3], Faudree and Gould showed that if a 2-connected graph contains no

K_{1, 3}

and P₆ as an induced subgraph, then the graph is hamiltonian. In this paper, we consider the extension of this result to cycles passing through specified vertices. We define the families of graphs which are extension of the forbidden pair

K_{1, 3}

and P₆, and prove that the forbidden families implies the existence of cycles passing through specified vertices.

Keywords

ENG

forbidden subgraph, cycle

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T. Sugiyama, Forbidden subgraphs and existence of cycles passing through specified vertices, in preparation.

Title

Pairs of forbidden class of subgraphs concerning K1,3 and P₆ to have a cycle containing specified vertices

Affiliations

Abstract

Keywords

Bibliography

Pairs of forbidden class of subgraphs concerning $K_{1, 3}$ and P₆ to have a cycle containing specified vertices