Exact Algorithms for the Graph Coloring Problem


  • Alane Marie de Lima Federal University of Paraná (UFPR)
  • Renato Carmo Federal University of Paraná (UFPR)




Graph Theory, Graph Coloring, Exact Algorithms


The graph coloring problem is the problem of partitioning the vertices of a graph into the smallest possible set of independent
sets. Since it is a well-known NP-Hard problem, it is of great interest of the computer science finding results over exact algorithms that solve it. The main algorithms of this kind, though, are scattered through the literature. In this paper, we group and contextualize some of these algorithms, which are based in Dynamic Programming, Branch-and-Bound and Integer Linear Programming. The algorithms for the first group are based in the work of Lawler, which searches maximal independent sets on each subset of vertices of a graph as the base of his algorithm. In the second group, the algorithms are based in the work of Brelaz, which adapted the DSATUR procedure to an exact version, and in the work of Zykov, which introduced the definition of Zykov trees. The third group contains the algorithms based in the work of Mehrotra and Trick, which uses the Column Generation method.


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How to Cite

de Lima, A. M., & Carmo, R. (2018). Exact Algorithms for the Graph Coloring Problem. Revista De Informática Teórica E Aplicada, 25(4), 57–73. https://doi.org/10.22456/2175-2745.80721



Special Issue - Exact and Heuristic Solutions for Optimization Problems