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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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Submitted on : Wednesday, July 4, 2018 - 10:36:09 AM
Last modification on : Wednesday, September 28, 2022 - 5:58:40 AM
Long-term archiving on: : Monday, October 1, 2018 - 10:56:46 AM


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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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