# Minimal graphs for 2-factor extension

august, 2020

Publication type:

Paper in peer-reviewed journals

Journal:

Discrete Applied Mathematics, vol. 282, pp. 65-79

Publisher:

Elsevier

HAL:

Keywords :

2-factor
Minimum expandable graph
Reliability

Abstract:

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).

BibTeX:

@article{Cos-DeW-Pic-2020, 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 }, month={8}, volume={282 }, pages={65--79}, }