Szemerédi's Regularity Lemma for matrices and sparse graphs

Details Szemerédi's Regularity Lemma for matrices and sparse graphs Szemerédi's Regularity Lemma for matrices and sparse graphs

2010-10-04

arxiv.org/abs/1010.0628v2

Mathematics

Combinatorics

Scientific paper

Szemer\'edi's Regularity Lemma is an important tool for analyzing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we prove a sparse Regularity Lemma that holds for all graphs. More generally, we give a Regularity Lemma that holds for arbitrary real matrices.

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