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# Nonpolyhedral Relaxations of Graph-Bisection Problems

@article{Poljak1995NonpolyhedralRO, title={Nonpolyhedral Relaxations of Graph-Bisection Problems}, author={Svatopluk Poljak and Franz Rendl}, journal={SIAM Journal on Optimization}, year={1995}, volume={5}, pages={467-487} }

- Published 1995 in SIAM Journal on Optimization
DOI:10.1137/0805024

We study the problem of nding the minimum bisection of a graph into two parts of prescribed sizes. We formulate two lower bounds on the problem by relaxing node-and edge-incidence vectors of cuts. We prove that both relaxations provide the same bound. The main fact we prove is that the duality between the relaxed edge-and node-vectors preserves very natural cardinality constraints on cuts. We present an analogous result also for the max-cut problem, and show a relation between the edge… CONTINUE READING

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