Add to ORKGAbstract. We determine the asymptotics of the independence number of the random d-regular graph for all d ě d0. It is highly concentrated, with constant-order fluctuations around nα ‹ ´ c ‹ logn for explicit constants α‹pdq and c‹pdq. Our proof rigorously confirms the one-step replica symmetry breaking heuristics for this problem, and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs. 1
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
Random regular graphs play a central role in combinatorics and theoretical computer science. In this...
AbstractLet α(Gn,p) denote the independence number of the random graph Gn,p. Let d=np. We show that ...
AbstractWe present algorithmic lower bounds on the size sd of the largest independent sets of vertic...
We consider the problem of finding a maximum independent set in a random graph. The random graph G i...
ABSTRACT: Random d-regular graphs have been well studied when d is fixed and the number of vertices ...
Abstract. This work is motivated by the long-standing open problem of designing a polynomial-time al...
The independence number of a sparse random graph G(n, m) of average degree d = 2m/n is well-known to...
In this paper, we develop efficient exact and approximate algorithms for computing a maximum indepen...
AbstractLet Gr denote a random r-regular graph with vertex set {1, 2, …, n} and α(Gr) and χ(Gr) deno...
A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either in...
Abstract. This work is motivated by the long-standing open problem of designing a polynomial-time al...
Studying independent sets of maximum size is equivalent to considering the hard-core model with the ...
Abstract. In this note, we study the independent domination number in the random graph G(n, p). We s...
For the Erdos-Rényi random graph Gn,p, we consider the order of a largest vertex subset that induces...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
Random regular graphs play a central role in combinatorics and theoretical computer science. In this...
AbstractLet α(Gn,p) denote the independence number of the random graph Gn,p. Let d=np. We show that ...
AbstractWe present algorithmic lower bounds on the size sd of the largest independent sets of vertic...
We consider the problem of finding a maximum independent set in a random graph. The random graph G i...
ABSTRACT: Random d-regular graphs have been well studied when d is fixed and the number of vertices ...
Abstract. This work is motivated by the long-standing open problem of designing a polynomial-time al...
The independence number of a sparse random graph G(n, m) of average degree d = 2m/n is well-known to...
In this paper, we develop efficient exact and approximate algorithms for computing a maximum indepen...
AbstractLet Gr denote a random r-regular graph with vertex set {1, 2, …, n} and α(Gr) and χ(Gr) deno...
A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either in...
Abstract. This work is motivated by the long-standing open problem of designing a polynomial-time al...
Studying independent sets of maximum size is equivalent to considering the hard-core model with the ...
Abstract. In this note, we study the independent domination number in the random graph G(n, p). We s...
For the Erdos-Rényi random graph Gn,p, we consider the order of a largest vertex subset that induces...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
Random regular graphs play a central role in combinatorics and theoretical computer science. In this...
AbstractLet α(Gn,p) denote the independence number of the random graph Gn,p. Let d=np. We show that ...