Results 11  20
of
15,573
Regular pairs in sparse random graphs I
 RANDOM STRUCTURES ALGORITHMS
, 2003
"... We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemeredi 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 ..."
Abstract

Cited by 21 (9 self)
 Add to MetaCart
We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemeredi 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
Hamiltonian Completions of Sparse Random Graphs
, 2012
"... Given a (directed or undirected) graph G, finding the smallest number of additional edges which make the graph Hamiltonian is called the Hamiltonian Completion Problem (HCP). We consider this problem in the context of sparse random graphs G(n,c/n) on n nodes, where each edge is selected independentl ..."
Abstract
 Add to MetaCart
Given a (directed or undirected) graph G, finding the smallest number of additional edges which make the graph Hamiltonian is called the Hamiltonian Completion Problem (HCP). We consider this problem in the context of sparse random graphs G(n,c/n) on n nodes, where each edge is selected
The Largest Eigenvalue of Sparse Random Graphs
 Combinatorics, Probability and Computing
, 2003
"... We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n, p) satisfies almost surely: 1 (G) = (1 + o(1)) maxf p ; npg, where is a maximal degree of G, and the o(1) term tends to zero as maxf p ; npg tends to infinity. ..."
Abstract

Cited by 35 (1 self)
 Add to MetaCart
We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n, p) satisfies almost surely: 1 (G) = (1 + o(1)) maxf p ; npg, where is a maximal degree of G, and the o(1) term tends to zero as maxf p ; npg tends to infinity.
The Cover Time of Sparse Random Graphs.
, 2003
"... We study the cover time of a random walk on graphs G 2 G n;p when p = ; c > 1. We prove that whp the cover time is asymptotic to c log n log n. ..."
Abstract

Cited by 31 (6 self)
 Add to MetaCart
We study the cover time of a random walk on graphs G 2 G n;p when p = ; c > 1. We prove that whp the cover time is asymptotic to c log n log n.
Sparse random graphs: Eigenvalues and eigenvectors
 ALGORITHMS
, 2013
"... In this paper we prove the semicircular law for the eigenvalues of regular random graph Gn,d in the case d→∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of ErdősRényi random graph G(n, p), answering a question raised by ..."
Abstract

Cited by 29 (4 self)
 Add to MetaCart
In this paper we prove the semicircular law for the eigenvalues of regular random graph Gn,d in the case d→∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of ErdősRényi random graph G(n, p), answering a question raised
Sparse Random Graphs Methods, Structure, and Heuristics
, 2007
"... This dissertation is an algorithmic study of sparse random graphs which are parametrized by the distribution of vertex degrees. Our contributions include: a formula for the diameter of various sparse random graphs, including the ErdősRényi random graphs Gn,m and Gn,p and certain powerlaw graphs; a ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This dissertation is an algorithmic study of sparse random graphs which are parametrized by the distribution of vertex degrees. Our contributions include: a formula for the diameter of various sparse random graphs, including the ErdősRényi random graphs Gn,m and Gn,p and certain powerlaw graphs
Rainbow Connection of Sparse Random Graphs
, 2012
"... An edge colored graph G is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this work we st ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
study the rainbow connectivity of binomial random graphs at log n+ω n the connectivity threshold p = where ω = ω(n) → ∞ and ω = o(log n) and of random rregular graphs where r � 3 is a fixed integer. Specifically, we prove that the rainbow connectivity rc(G) of G = G(n, p) satisfies rc(G) ∼ max{Z1
The strong edge colorings of a sparse random graph
 Australasian Journal of Combinatorics
, 1998
"... The strong chromatic index of a graph G is the smallest integer k such that the edge set E ( G) can be partitioned into k induced subgraphs of G which form matchings. In this paper we consider the behavior of the strong chromatic index of a sparse random graph K (n, p), where p = p(n) = 0(1). 1. ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
The strong chromatic index of a graph G is the smallest integer k such that the edge set E ( G) can be partitioned into k induced subgraphs of G which form matchings. In this paper we consider the behavior of the strong chromatic index of a sparse random graph K (n, p), where p = p(n) = 0(1). 1.
Results 11  20
of
15,573