Critical hereditary graph classes: a survey
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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.
KeywordsComputational complexity Polynomial-time algorithm Hereditary graph class Independent set problem Dominating set problem Coloring problem List edge-ranking problem
The research is partially supported by LATNA laboratory, National Research University Higher School of Economics, RF government Grant, ag. 11.G34.31.00357, and by Russian Foundation for Basic Research, Grant 14-01-00515-a, by the grant of President of Russian Federation MK-4819.2016.1.
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