Extremal graphs having no matching cuts.

A graph G = (V, E) is matching immune if there is no matching cut in G. We show that for any matching immune graph G, vertical bar E vertical bar >= inverted right perpendicular3 (vertical bar V vertical bar-1)/2inverted left perpendicular. This bound is tight, as we define operations that construct, from a given vertex, exactly the class of matching immune graphs that attain the bound. (C) 2011 Wiley Periodicals, Inc. J Graph Theory 69:206-222, 2012 .