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 Exp2(n). We give an explicit formula for Exp2(n) and provide 2-factor expandable graphs of minimum size Exp2(n).
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