2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 135138
author:  Paul Bonsma 

title:  A characterization of extremal graphs with no matchingcut 
keywords:  matchingcut, 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(V1)/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 matchingcut, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 135138 
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