Bipartite Subgraphs of Triangle-Free Graphs
SIAM Journal on Discrete Mathematics
The size of the largest bipartite subgraphs
Discrete Mathematics
Judicious partitions of 3-uniform hypergraphs
European Journal of Combinatorics
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Problems and results on judicious partitions
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Maximum cuts and judicious partitions in graphs without short cycles
Journal of Combinatorial Theory Series B
The RPR2 rounding technique for semidefinite programs
Journal of Algorithms
Maximizing Several Cuts Simultaneously
Combinatorics, Probability and Computing
Judicious partitions of bounded-degree graphs
Journal of Graph Theory
On several partitioning problems of Bollobás and Scott
Journal of Combinatorial Theory Series B
Partitioning 3-uniform hypergraphs
Journal of Combinatorial Theory Series B
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A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most 1, and its size is the number of edges which go across the two parts. In this paper, motivated by several questions and conjectures of Bollobas and Scott, we study maximum bisections of graphs. First, we extend the classical Edwards bound on maximum cuts to bisections. A simple corollary of our result implies that every graph on n vertices and m edges with no isolated vertices, and maximum degree at most n/3+1, admits a bisection of size at least m/2+n/6. Then using the tools that we developed to extend Edwards@?s bound, we prove a judicious bisection result which states that graphs with large minimum degree have a bisection in which both parts span relatively few edges. A special case of this general theorem answers a conjecture of Bollobas and Scott, and shows that every graph on n vertices and m edges of minimum degree at least 2 admits a bisection in which the number of edges in each part is at most (1/3+o(1))m. We also present several other results on bisections of graphs.