Then it can be shown, via König's theorem, that "G"' has a matching of size "m" if and only if there exists "n"-"m" paths that cover each vertex in "G", where "n" is the number of vertices in "G".
Then it can be shown that "G"' has a matching of size "m" if and only if there exists "n"-"m" paths that cover each vertex in "G", where "n" is the number of vertices in "G".