A closure concept in factor-critical graphs

Authors:
Tsuyoshi Nishimura
Affiliations:
Department of Mathematics, Shibaura Institute of Technology, Fukasaku, Saitama 330-8570, Japan
Venue:
Discrete Mathematics
Year:
2002

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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 {u, υ} be a pair of vertices in V(G) - {x} such that uυ ∈ E(G), x ∈ NG(u) ∩ NG(υ), and NG(x) ⊂ NG(u) ∪ NG(υ) ∪ {u, υ}. Then G is n-factor-critical if and only if G + uυ is n-factor-critical.