yields True if the edge list elist is an independent edge set of the graph g, and False otherwise.
- 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.
Examplesopen allclose all
IndependentEdgeSetQ works with large graphs:
Enumerate all independent edge sets for a cycle graph:
Enumerate all subsets of edges and select the independent edge 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:
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:
Wolfram Research (2010), IndependentEdgeSetQ, Wolfram Language function, https://reference.wolfram.com/language/ref/IndependentEdgeSetQ.html (updated 2014).
Wolfram Language. 2010. "IndependentEdgeSetQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/IndependentEdgeSetQ.html.
Wolfram Language. (2010). IndependentEdgeSetQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IndependentEdgeSetQ.html