Publication

On the connectivity of visibility graphs

2011
Reports

Abstract

The visibility graph of a finite set of points in the plane has the points as vertices and an edge between two vertices if the line segment between them contains no other points. This paper establishes bounds on the edge- and vertex-connectivity of visibility graphs. Unless all its vertices are collinear, a visibility graph has diameter at most 2, and so it follows by a result of Plesn'ik (1975) that its edge-connectivity equals its minimum degree. We strengthen the result of Plesn'ik by showing that for any two vertices v and w in a graph of diameter 2, if deg(v)

Official source

https://infoscience.epfl.ch/entities/publication/ba4e7dfb-a85f-43f9-b205-055be219955f

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2011
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ba4e7dfb-a85f-43f9-b205-055be219955f

About this result

Related concepts (32)

K-edge-connected graph

In graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph is the largest k for which the graph is k-edge-connected. Edge connectivity and the enumeration of k-edge-connected graphs was studied by Camille Jordan in 1869. Let be an arbitrary graph. If the subgraph is connected for all where , then G is said to be k-edge-connected. The edge connectivity of is the maximum value k such that G is k-edge-connected.

Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v.

Edge cover

In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. In computer science, the minimum edge cover problem is the problem of finding an edge cover of minimum size. It is an optimization problem that belongs to the class of covering problems and can be solved in polynomial time. Formally, an edge cover of a graph G is a set of edges C such that each vertex in G is incident with at least one edge in C.

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