LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Matchings Meeting Quotas and their Impact on the Blow-Up Lemma

A bipartite graph G = (U, V ; E) is called #-regular if the edge density of every su#ciently large induced subgraph di#ers from the edge density of G by no more than #. If, in addition, the degree of each vertex in G is between (d #)n and (d + #)n, where d is the edge density of G and = n, then G is called super (d, #)-regular. In [Combinatorica, 19 (1999), pp. 437-- 452] it was shown that if S U and T V are subsets of vertices in a super-regular bipartite graph G = (U, V ; E), and if a perfect matching M of G is chosen randomly, then the number of edges of M that go between the sets S and T is roughly |S||T |/n. In this paper