... obvious thatinner matchings selected within Aimay leave at most√ǫn vertices of Aiuncovered. Sinceone uses at most seven crossing and inner matchings in the proof of Claim 1 and in allsubsequent ... edges in the complete bipartite graphs B(A1, A2) and B(A3, A4) are colored 1, in B(A1, A3) and B(A2, A4) are colored 2, and B(A1, A4) and in B(A2, A3) are colored 3. Inside ... even, since n is even) and let Z be the union of their|X| − |Y | endpoints and Y , |Z| = |X|. Let M2be a maximum matching in B(Z, X) in color 2. Since we assumed that X is connected in G2,...