Journal of Combinatorial Optimization

, Volume 33, Issue 3, pp 809–813 | Cite as

Polynomial-time approximation algorithms for the coloring problem in some cases

Article
First Online:

Abstract

We consider the coloring problem for hereditary graph classes, i.e. classes of simple unlabeled graphs closed under deletion of vertices. For the family of the hereditary classes of graphs defined by forbidden induced subgraphs with at most four vertices, there are three classes with an open complexity of the problem. For the problem and the open three cases, we present approximation polynomial-time algorithms with performance guarantees.

Keywords

Coloring problem Computational complexity  Approximation algorithm Performance guarantee 
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Notes

Acknowledgments

This article is partially supported by Russian Foundation for Basic Research, Grants 16-31-60008-mol-a-dk and 16-01-00599-a; by RF President Grant MK-4819.2016.1; by LATNA laboratory, National Research University Higher School of Economics.

References

  1. Alekseev V (2004) Polynomial algorithm for finding the largest independent sets in graphs without forks. Discret Appl Math 135(1–3):3–16Google Scholar
  2. Edmonds J (1965) Paths, trees, and flowers. Can J Math 17:449–467MathSciNetCrossRefMATHGoogle Scholar
  3. Lozin V, Malyshev D (2015) Vertex coloring of graphs with few obstructions. Discret Appl Math. doi: 10.1016/j.dam.2015.02.015

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

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

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