Geodesic
A characterization of extremal graphs with no matching-cut
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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 $G=(V,E)$, $|E|≥\lceil 3(|V|-1)/2\rceil$ , 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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     author = {Bonsma, Paul},
     title = {A characterization of extremal graphs with no matching-cut},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3398/}
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Bonsma, Paul. A characterization of extremal graphs with no matching-cut. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3398. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3398/

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