Publication

Bicolored matchings in some classes of graphs

Dominique de Werra, Bernard Ries
2007
Journal Articles

Abstract

We consider the problem of finding in a graph a set $R$ of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with $n$ nodes on each side, we give sufficient conditions for the existence of a set $R$ with $|R| = n + 1$ such that perfect matchings with $k$ red edges exist for all $k, 0\le k\le n$ . Given two integers $p

Official source

https://infoscience.epfl.ch/entities/publication/a3074e82-7cb1-43de-b212-ac5f9e786b2f

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Dominique de Werra, Bernard Ries
2007
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a3074e82-7cb1-43de-b212-ac5f9e786b2f

About this result

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Line graph

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.

Perfect matching

In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G = (V, E), a perfect matching in G is a subset M of edge set E, such that every vertex in the vertex set V is adjacent to exactly one edge in M. A perfect matching is also called a 1-factor; see Graph factorization for an explanation of this term. In some literature, the term complete matching is used. Every perfect matching is a maximum-cardinality matching, but the opposite is not true.

Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.

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