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Regular version of the site

Article

Critical hereditary graph classes: a survey

Optimization Letters. 2016. Vol. 10. No. 8. P. 1593-1612.

The task of complete complexity dichotomy is to clearly distinguish between easy and hard cases of a given problem on a family of subproblems. We consider this task for some optimization problems restricted to certain classes of graphs closed under deletion of vertices. A concept in the solution process is based on revealing the so-called “critical” graph classes, which play an important role in the complexity analysis for the family. Recent progress in studying such classes is presented in the article.