Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 171-175 |
| Number of pages | 5 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 32 |
| Publication status | Published - 2005 Dec 1 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
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Cite this
Nishimura, T. (2005). Note on a closure concept and matching extension. Australasian Journal of Combinatorics, 32, 171-175.