The first cycles in an evolving graph
Discrete Mathematics
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Satisfiability threshold for random XOR-CNF formulas
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Some optimal inapproximability results
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Counting connected graphs inside-out
Journal of Combinatorial Theory Series B
Random MAX SAT, random MAX CUT, and their phase transitions
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part II
Solving Sparse Random Instances of Max Cut and Max 2-CSP in Linear Expected Time
Combinatorics, Probability and Computing
MAX k-CUT and approximating the chromatic number of random graphs
Random Structures & Algorithms
Analytic Combinatorics
Limit theorems for random MAX-2-XORSAT
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Hi-index | 0.00 |
A k-cut of a graph G = (V, E) is a partition of its vertex set into k parts; the size of the k-cut is the number of edges with endpoints in distinct parts. MAX-k-CUT is the optimization problem of finding a k-cut of maximal size and the case where k = 2 (often called MAX-CUT) has attracted a lot of attention from the research community. MAX-CUT---more generally, MAX-k-CUT--- is NP-hard and it appears in many applications under various disguises. In this paper, we consider the MAX-CUT problem on random connected graphs C(n, m) and on Erdös-Rényi random graphs G(n, m). More specifically, we consider the distance from bipartiteness of a graph G = (V,E), the minimum number of edge deletions needed to turn it into a bipartite graph. If we denote this distance DistBip(G), the size of the MAX-CUT of a graph G = (V, E) is clearly given by |E| -- DistBip(G). Fix ε 0. For random connected graphs, we prove that asymptotically almost surely (a.a.s) DistBip (C(n, m)) ~ m-n/4 whenever m = n + O(n1−ε). For sparse random graphs G(n, m = n/2 + un2/3/2) we show that DistBip (G(n, m)) is a.a.s about (2m-n)3/6n2 + 1/12 log n − 1/4 log μ for any 1 O(n1/3−ε).