A closure concept in factor-critical graphs

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A graph G is called n-factor-critical if the removal of every set of n vertices results in a graph with a 1-factor. We prove the following theorem: Let G be a graph and let x be a locally n-connected vertex. Let {μ, v} be a pair of vertices in V(G) - {x} such that uv E(G), x ∈ NG(u) ∩ NG(v), and NG(x) ⊂ NG(u) ∪ NG(v) ∪ {u,v}. Then G is n-factor-critical if and only if G + uv is n-factor-critical.

Original languageEnglish
Pages (from-to)319-324
Number of pages6
JournalDiscrete Mathematics
Volume259
Issue number1-3
Publication statusPublished - 2002 Dec 28

Keywords

  • 1-Factors
  • Closures
  • Factor-critical graphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

A closure concept in factor-critical graphs. / Nishimura, Tsuyoshi.

In: Discrete Mathematics, Vol. 259, No. 1-3, 28.12.2002, p. 319-324.

Research output: Contribution to journalArticle

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