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A Note on Extendability and Factor-Criticality
Qinglin Yu
Department of Mathematics and Statistics, University College of The Cariboo, Kamloops, B.C. Canada
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P.R. China
yu@cariboo.bc.ca
Annals of Combinatorics 6 (3) p.479-481 September, 2002
AMS Subject Classification: 05C70
Abstract:
Let n be a non-negative integer. A graph G is said to be n- factor-critical if the subgraph G - S has a perfect matching for any subset S of V(G) with |S| = n. In this paper, we provide much shorter proofs of two main theorems about extendability and factor-criticality obtained by Favaron [2]. Furthermore, we present a solution to an open problem posted in the same paper.
Keywords: matching, k-extendable graphs, n-factor-critical graphs

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