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Optimization Letters

, Volume 10, Issue 8, pp 1593–1612 | Cite as

Critical hereditary graph classes: a survey

  • D. S. MalyshevEmail author
  • P. M. Pardalos
Review Article

Abstract

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.

Keywords

Computational complexity Polynomial-time algorithm  Hereditary graph class Independent set problem Dominating set problem Coloring problem List edge-ranking problem 

Notes

Acknowledgments

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsNizhny NovgorodRussia
  2. 2.University of FloridaGainesvilleUSA

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