Quasi-random graphs

  title={Quasi-random graphs},
  author={Fan Chung Graham and Ronald L. Graham and Richard M. Wilson},
We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class. 
A note on the relation between two properties of random graphs
The $t$-e.c. and pseudo-random property are typical properties of random graphs. In this note, we study the gap between them which has not been studied well. As a main result, we give the first
We show that every quasi-random graph with vertices and minimum degree has diameter either 2 or 3 and that every quasi-random graph with n vertices has a clique number of with wide spread.
3-Symmetric Graphs
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs
Quasi-random classes of hypergraphs
  • F. Chung
  • Mathematics, Computer Science
  • 1990
This work investigates the relations among a number of different graph properties for k-uniformhypergraphs, which are shared by random hypergraphs and form equivalence classes which constitute a natural hierarchy.
Generalized quasirandom graphs
It is well known that a random graph G1=2(n) is Hamil- tonian almost surely. In this paper, we show that every quasi- random graph G(n) with minimum degree (1 + o(1))n=2 is also Hamiltonian.
The asymptotics of strongly regular graphs
A strongly regular graph is called trivial if it or its complement is a union of disjoint cliques. We prove that every infinite family of nontrivial strongly regular graphs is quasi-random in the
Pseudo-random properties of self-complementary symmetric graphs
There are some results in the literature showing that Paley graphs behave in many ways like random graphs G(n, 1-2). In this paper, we extend these results to the other family of self-complementary
Quasirandom Multitype Graphs
The notion of quasirandom graphs has received much attention in the last decades, but here the idea is that a graph need only satisfy certain properties, without direction, loops, or multiple edges.
Tree-minimal graphs are almost regular
This conjecture is known to hold for several classes of graphs F , including forests, even cycles, and complete bipartite graphs [7], Boolean cubes [5] and bipartite graphs F which contain a vertex


Quasi-Random Hypergraphs
A large equivalence class of properties shared by most hypergraphs, including so-called random hyper graphs, are described, which shows that many global properties of hyperGraphs are actually consequences of simple local conditions.
Pseudo-Random Graphs
Explicit construction of linear sized tolerant networks
Intersection theorems with geometric consequences
It is proved that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℽ there is one set within which all the distances are realised.
A Constructive Solution to a Tournament Problem
By a tournament Tn on n vertices, we shall mean a directed graph on n vertices for which every pair of distinct vertices form the endpoints of exactly one directed edge (e.g., see [5]). If x and y
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value