Regular pairs in sparse random graphs I
نویسندگان
چکیده
We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemerédi and, among other things, show that they must satisfy a certain local pseudorandom property. This property and its consequences turn out to be useful when considering embedding problems in subgraphs of sparse random graphs.
منابع مشابه
Counting Small Cliques in 3-uniform Hypergraphs
Many applications of Szemerédi’s Regularity Lemma for graphs are based on the following counting result. If G is an s-partite graph with partition V (G) = ⋃s i=1 Vi, |Vi| = m for all i ∈ [s], and all pairs (Vi, Vj ), 1 i < j s, are -regular of density d, then G contains (1± f( ))d s 2 ms cliques Ks, provided < (d), where f( ) tends to 0 as tends to 0. Guided by the regularity lemma for 3-unifor...
متن کاملThe Regularity Lemma of Szemerédi for Sparse Graphs
In this note we present a new version of the well-known lemma of Szemerédi [17] concerning regular partitions of graphs. Our result deals with subgraphs of pseudo-random graphs, and hence may be used to partition sparse graphs that do no contain dense subgraphs.
متن کاملSparse Regular Random Graphs: Spectral Density and Eigenvectors
We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges to the semicircle law. Moreover, we prove concentration estimates on the number of eigenvalues over progressi...
متن کاملThe diameter of random regular graphs
We give asymptotic upper and lower bounds for the diameter of almost every r-regular graph on n vertices (n~). Though random graphs of various types have been investigated extensively over the last twenty years, random regular graphs have hardly been studied. The reason for this is that until recently there was no formula for the asymptotic number of labelled r-regular graphs of order n. Such a...
متن کاملQuasi-randomness and Algorithmic Regularity for Graphs with General Degree Distributions
We deal with two intimately related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph “resembles” a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which ex...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Random Struct. Algorithms
دوره 22 شماره
صفحات -
تاریخ انتشار 2003