Authors

Citation

V. Rodl et al., Matchings meeting quotas and their impact in the blow-up lemma, SIAM J COMP, 31(2), 2001, pp. 428-446

Citations number

17

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Computer Science & Engineering

Journal title

SIAM JOURNAL ON COMPUTING

ISSN journal

0097-5397
â†’ ACNP

Volume

31

Issue

2

Year of publication

2001

Pages

428 - 446

Database

ISI

SICI code

0097-5397(20011011)31:2<428:MMQATI>2.0.ZU;2-C

Abstract

A bipartite graph G = (U,V;E) is called epsilon -regular if the edge densit
y of every sufficiently large induced subgraph differs from the edge densit
y of G by no more than. 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 a
nd |U| = |V| = n, then G is called super (d,epsilon)-regular. In [Combinato
rica, 19(1999), pp. 437-452] it was shown that if S subset ofU and T subset
ofV 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 o
f 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 condi
tional probabilities. As an application, we give an alternative constructiv
e proof of the blow-up lemma of Komlos, Sarkozy, and Szemeredi (see [ Combi
natorica, 17 (1997), pp. 109-123] and [Random Structures Algorithms, 12 (19
98), pp. 297-312]).