2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 135-138
| author: | Paul Bonsma |
|---|---|
| title: | A characterization of extremal graphs with no matching-cut |
| keywords: | matching-cut, matching immune, extremal graphs |
| 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.
|
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| reference: | Paul Bonsma (2005), A characterization of extremal graphs with no matching-cut, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 135-138 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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Automatically produced on Di Sep 27 10:09:49 CEST 2005 by gustedt
