DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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A characterization of extremal graphs with no matching-cut

Paul Bonsma


A graph is called (matching-)immune if it has no edge cut that is also a matching. Farley and Proskurowski proved that for all immune graphs G=(V,E), |E|≥⌈3(|V|-1)/2⌉, and constructed a large class of immune graphs that attain this lower bound for every value of |V(G)|, called ABC graphs. They conjectured that every immune graph that attains this lower bound is an ABC graph. We present a proof of this conjecture.

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