Note on a closure concept and matching extension

研究成果: Article査読

抄録

We prove the following theorems: (i) Let G be a graph and let x be a locally 2n-connected vertex. Let {u,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 if G + uv is n-extendable, then G is n-extendable or G is a member of the exceptional family F of graphs described. (ii) Let G be a (2n + l)-connected graph. Let {u,v,x} be a three-vertex subset of V(G) such that uv ∉ E(G), x ∈ NG(u) ∩ NG(v), and NG(x) ⊂ NG(u) ∪ NG(v) ∪ {u,v}. If G + uv is n-extendable, then G is n-extendable or G is a member of the exceptional family F of graphs described.

本文言語English
ページ(範囲)171-175
ページ数5
ジャーナルAustralasian Journal of Combinatorics
32
出版ステータスPublished - 2005

ASJC Scopus subject areas

  • 離散数学と組合せ数学

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