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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 7863650, 6 pages
Research Article

On Graphs of the Cone Decompositions for the Min-Cut and Max-Cut Problems

Department of Discrete Analysis, P.G. Demidov Yaroslavl State University, Sovetskaya 14, Yaroslavl 150000, Russia

Received 13 August 2015; Accepted 8 December 2015

Academic Editor: Frank Werner

Copyright © 2016 Vladimir Bondarenko and Andrei Nikolaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider maximum and minimum cut problems with nonnegative weights of edges. We define the graphs of the cone decompositions and find a linear clique number for the min-cut problem and a superpolynomial clique number for the max-cut problem. These values characterize the time complexity in a broad class of algorithms based on linear comparisons.