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Journal Articles Discrete Applied Mathematics Year : 2018

Minimal graphs for matching extension

Abstract

Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = |V |, what is the minimum cardinality of E such that there exists G = (V, E) which is 2-factor expandable? This minimum number is denoted by Exp 2 (n). We give an explicit formula for Exp 2 (n) and provide 2-factor expandable graphs of minimum size Exp 2 (n).
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Dates and versions

hal-01829546 , version 1 (04-07-2018)

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Marie-Christine Costa, Dominique de Werra, Christophe Picouleau. Minimal graphs for matching extension. Discrete Applied Mathematics, 2018, 234, pp.47-55. ⟨10.1016/j.dam.2015.11.007⟩. ⟨hal-01829546⟩
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