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.
|Name||DMTCS Proceedings Series|
|Conference||European Conference on Combinatorics, Graph Theory and Applications, EuroComb '05|
|Period||5/09/09 → 9/09/09|
|Other||September 5-9, 2009|
- matching immune
- extremal graphs