A characterization of extremal graphs with no matching-cut

P.S. Bonsma

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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|≥⌈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.
Original languageUndefined
Title of host publicationEuropean Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
EditorsS. Felsner
Place of PublicationNancy, France
PublisherDMTCS
Pages135-138
Number of pages4
Publication statusPublished - 2005
EventEuropean Conference on Combinatorics, Graph Theory and Applications, EuroComb '05 - Berlin, Germany
Duration: 5 Sep 20099 Sep 2009

Publication series

NameDMTCS Proceedings Series
PublisherDMTCS
VolumeAE
ISSN (Print)1365-8050

Conference

ConferenceEuropean Conference on Combinatorics, Graph Theory and Applications, EuroComb '05
Period5/09/099/09/09
OtherSeptember 5-9, 2009

Keywords

  • IR-72727
  • METIS-226878
  • matching immune
  • extremal graphs
  • Matching-cut

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