Szemerédi's Regularity Lemma and Its Applications in Graph Theory
ثبت نشده
چکیده
منابع مشابه
Szemerédi's regularity lemma revisited
Szemerédi’s regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemerédi’s theorem on arithmetic progressions [19], [18]. In this note we revisit this lemma from the perspective of probability theory and information theory instead of graph theory, and observe a slightly stronger variant of this lemma, related to ...
متن کاملSzemerédi's Regularity Lemma and Its Applications to Pairwise Clustering and Segmentation
Szemerédi’s regularity lemma is a deep result from extremal graph theory which states that every graph can be well-approximated by the union of a constant number of random-like bipartite graphs, called regular pairs. Although the original proof was non-constructive, efficient (i.e., polynomial-time) algorithms have been developed to determine regular partitions for arbitrary graphs. This paper ...
متن کاملRevealing structure in large graphs: Szemerédi's regularity lemma and its use in pattern recognition
Introduced in the mid-1970’s as an intermediate step in proving a long-standing conjecture on arithmetic progressions, Szemerédi’s regularity lemma has emerged over time as a fundamental tool in different branches of graph theory, combinatorics and theoretical computer science. Roughly, it states that every graph can be approximated by the union of a small number of random-like bipartite graphs...
متن کاملSzemerédi's Regularity Lemma for Matrices and Sparse Graphs
Szemerédi’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.
متن کاملA proof of the stability of extremal graphs, Simonovits' stability from Szemerédi's regularity
The following sharpening of Turán’s theorem is proved. Let Tn,p denote the complete p– partite graph of order n having the maximum number of edges. If G is an n-vertex Kp+1-free graph with e(Tn,p) − t edges then there exists an (at most) p-chromatic subgraph H0 such that e(H0) ≥ e(G)− t. Using this result we present a concise, contemporary proof (i.e., one using Szemerédi’s regularity lemma) fo...
متن کامل