On the independence number of random graphs
Discrete Mathematics
Expected complexity of graph partitioning problems
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Coloring random and semi-random k-colorable graphs
Journal of Algorithms
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Approximating the independence number via the j -function
Mathematical Programming: Series A and B
Finding a large hidden clique in a random graph
proceedings of the eighth international conference on Random structures and algorithms
Finding and certifying a large hidden clique in a semirandom graph
Random Structures & Algorithms
Heuristics for semirandom graph problems
Journal of Computer and System Sciences
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Exact and approximative algorithms for coloring G(n,p)
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
The Lovász Number of Random Graphs
Combinatorics, Probability and Computing
Solving NP-hard semirandom graph problems in polynomial expected time
Journal of Algorithms
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We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. Let $G_{n,p}$ be a random graph, and let $S$ be a set of $k$ vertices, chosen uniformly at random. Then, let $G_0$ be the graph obtained by deleting all edges connecting two vertices in $S$. Finally, an adversary may add edges to $G_0$ that do not connect two vertices in $S$, thereby producing the instance $G=G_{n,p,k}^*$. We present an algorithm that on input $G=G_{n,p,k}^*$ finds an independent set of size $\geq k$ within polynomial expected time, provided that $k\geq C(n/p)^{1/2}$ for a certain constant $C0$. Moreover, we prove that in the case $k\leq (1-\varepsilon)\ln(n)/p$ this problem is hard.