Publication

Minimal graphs for 2-factor extension

Dominique de Werra
2020
Journal Articles

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 = vertical bar V vertical bar, 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). (C) 2019 Elsevier B.V. All rights reserved.

Official source

https://infoscience.epfl.ch/entities/publication/b75f0da0-baae-495c-9035-2e08459c0a50

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Dominique de Werra
2020
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b75f0da0-baae-495c-9035-2e08459c0a50

About this result

Related concepts (32)

Chordal graph

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree.

List of graphs

This partial list of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see . Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer.

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In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.

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