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On \(k\)-factor-critical graphs. (English) Zbl 0865.05061

Summary: A graph is said to be \(k\)-factor-critical if the removal of any set of \(k\) vertices results in a graph with a perfect matching. We study some properties of \(k\)-factor-critical graphs and show that many results on \(q\)-extendable graphs can be improved using this concept.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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