Minimal graphs for 2-factor extension

Marie-Christine Costa, Dominique de Werra and Christophe Picouleau
august, 2020
Publication type:
Paper in peer-reviewed journals
Discrete Applied Mathematics, vol. 282, pp. 65-79
Keywords :
2-factor Minimum expandable graph Reliability
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 = Card 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).
    author={Marie-Christine Costa and Dominique de Werra and Christophe 
           Picouleau },
    title={Minimal graphs for 2-factor extension },
    doi={10.1016/j.dam.2019.11.022 },
    journal={Discrete Applied Mathematics },
    year={2020 },
    volume={282 },