# IndependentEdgeSetQ

IndependentEdgeSetQ[g,elist]

yields True if the edge list elist is an independent edge set of the graph g, and False otherwise.

# Details • An independent edge set is a set of edges that are never incident to the same vertex.
• An independent edge set is also known as a matching.
• IndependentEdgeSetQ works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

open allclose all

## Basic Examples(1)

Test whether a set of edges is an independent edge set:

## Scope(5)

Test undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

IndependentEdgeSetQ works with large graphs:

## Applications(2)

Enumerate all independent edge sets for a cycle graph:

Enumerate all subsets of edges and select the independent edge sets:

Highlight independent sets:

Enumerate all maximal independent edge sets for a wheel graph:

Find the length of a maximal independent edge set:

Enumerate all edge subsets of length 2 and select the independent edge sets:

Highlight maximal independent sets:

## Properties & Relations(3)

A largest independent edge set can be found using FindIndependentEdgeSet:

Bipartite graphs have independent edge sets and vertex covers of equal length:

For a graph without isolated vertices, the sum of the size of the independent edge set and the size of the edge cover equals the number of vertices: