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Publication

Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

Dominique de Werra, Bernard Ries
2010
Journal Articles

Abstract

Given an undirected graph G = (V, E) with matching number nu(G), a d-blocker is a subset of edges B such that nu((V, E \ B)) = d. While the associated decision problem is NP-complete in bipartite graphs we show how to construct efficiently minimum d-transversals and minimum d-blockers in the special cases where G is a grid graph or a tree. (C) 2009 Elsevier B.V. All rights reserved.

Official source

https://infoscience.epfl.ch/entities/publication/06bddac1-ff26-4876-983f-334cf4f36f99

About this result

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Dominique de Werra, Bernard Ries
2010
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/06bddac1-ff26-4876-983f-334cf4f36f99

About this result

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Matching (graph theory)

In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite graph can be treated as a network flow problem. Given a graph G = (V, E), a matching M in G is a set of pairwise non-adjacent edges, none of which are loops; that is, no two edges share common vertices.

Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in red, each edge has endpoints of differing colors, as is required in the graph coloring problem.

Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. In formal terms, a directed graph is an ordered pair where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.

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Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

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