Factor-critical graph

Factor-critical graph

In graph theory, a mathematical discipline, factor-critical graph is a graph with "n" vertices in which any subset of "n" − 1 vertices has a perfect matching. For example, any odd-length cycle graph is factor-critical.

Factor-critical graphs must always have an odd number of vertices, and cannot be bipartite.

A blossom is a factor-critical subgraph of a graph. Blossoms play a key role in Jack Edmonds' algorithms for maximum matching and minimum weight perfect matching in non-bipartite graphs.

References

*cite journal | author=Edmonds, Jack | authorlink = Jack Edmonds | title=Paths, Trees and Flowers | journal=Canadian J. Math | volume=17 | year=1965 | pages=449–467 | id = MathSciNet | id = 0177907


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