Equivalence between Extendibility and Factor-Criticality

Details Equivalence between Extendibility and Factor-Criticality Equivalence between Extendibility and Factor-Criticality

2010-11-15

arxiv.org/abs/1011.3381v1

Ars Combinatoria, 85(2007), 279-285

Mathematics

Combinatorics

This paper has been published at Ars Combinatoria

Scientific paper

In this paper, we show that if $k\geq (\nu+2)/4$, where $\nu$ denotes the order of a graph, a non-bipartite graph $G$ is $k$-extendable if and only if it is $2k$-factor-critical. If $k\geq (\nu-3)/4$, a graph $G$ is $k\ 1/2$-extendable if and only if it is $(2k+1)$-factor-critical. We also give examples to show that the two bounds are best possible. Our results are answers to a problem posted by Favaron [3] and Yu [11].

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