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- W2060542023 abstract "A bipartite graph G = (U,V;E) is called $epsilon$-regular if the edge density of every sufficiently large induced subgraph differs from the edge density of G by no more than $epsilon$. If, in addition, the degree of each vertex in G is between $(d-epsilon)n$ and $(d+epsilon)n$, where d is the edge density of G and |U|=|V|=n, then G is called super $(d,epsilon)$-regular. In [Combinatorica, 19 (1999), pp. 437--452] it was shown that if $S subset U$ and $T subset V$ 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, we derandomize this result using the Erdos--Selfridge method of conditional probabilities. As an application, we give an alternative constructive proof of the blow-up lemma of $komlos$, $sarkozy$, and $szemeredi$ (see [Combinatorica, 17 (1997), pp. 109--123] and [Random Structures Algorithms, 12 (1998), pp. 297--312])." @default.
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- W2060542023 date "2001-01-01" @default.
- W2060542023 modified "2023-10-17" @default.
- W2060542023 title "Matchings Meeting Quotas and Their Impact on the Blow-Up Lemma" @default.
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- W2060542023 doi "https://doi.org/10.1137/s0097539700371053" @default.
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