User talk:131.220.249.230

Corollary 1 seems to be formulated incorrectly. Consider for example the graph with 4 vertices and 4 edges that is shaped like a square. Then we have a maximum matching M consiting of both horizontal edges. Now a path consisting of one horizontal and one vertical edge has even lenght and its edges alternate between being in M and not being in M. But constructing the new set M' as explained in the corollary clearly does not give us a new maximum matching, as M' is not even a matching.