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A characterization of extremal graphs without matching-cuts

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Bonsma, P.S. (2005) A characterization of extremal graphs without matching-cuts. [Report]

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Abstract: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 $G=(V,E)$, $|E|\geq \lceil 3(|V|-1)/2\rceil$, and constructed a large class of immune graphs attaining this lower bound for every value of $|V(G)|$, called ABC graphs. In this paper, we prove their conjecture that every immune graph that attains this lower bound is an ABC graph.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65953
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