Coloring

Chapter
Part of the Texts in Computer Science book series (TCS)

Abstract

Coloring in a graph refers either to vertex coloring, edge coloring or both in which case it is called total coloring. Each vertex is assigned a color from a set of colors such that no two adjacent vertices have the same color in vertex coloring. Edge coloring is the process of assigning colors to the edges of a graph such that no two edges incident to the same vertex are assigned the same color. We review sequential, parallel, and distributed algorithms for vertex and edge coloring in this chapter.

References

  1. 1.
    Allwright JR, Bordawekar R, Coddington PD, Dincer K, Martin CL (1995) A comparison of parallel graph coloring algorithms. Technical report SCCS-666, Northeast Parallel Architecture Center, Syracuse UniversityGoogle Scholar
  2. 2.
    Barenboim L, Elkin M (2013) Distributed graph coloring. Monograph, Ben Gurion University of the NegevGoogle Scholar
  3. 3.
    Brelaz D (1979) New methods to color the vertices of a graph. Commun ACM 22(4):251–256MathSciNetCrossRefGoogle Scholar
  4. 4.
    Brooks RL (1941) On colouring the nodes of a network. Proc Camb Philos Soc Math Phys Sci 37:194–197MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cole R, Vishkin U (1986) Deterministic coin tossing with applications to optimal parallel list ranking. Inf Control 70(1):32–53MathSciNetCrossRefGoogle Scholar
  6. 6.
    Coleman TF, More JJ (1983) Estimation of sparse Jacobian matrices and graph coloring problems. SIAM J Numer Anal 20(1):187–209MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gandham S, Dawande M, Prakash R (2005) Link scheduling in sensor networks: distributed edge coloring revisited. In: Proceedings of the 24th INFOCOM, vol 4, pp 2492–2501Google Scholar
  8. 8.
    Garey MR, Johnson DS (1979) Computers and intractability. W.H. Freeman, New YorkMATHGoogle Scholar
  9. 9.
    Gebremedhin AH (1999) Parallel graph coloring. MS thesis, Department of Informatics University of Bergen NorwayGoogle Scholar
  10. 10.
    Grable D, Panconesi A (1997) Nearly optimal distributed edge-coloring in \(O(\log {\log {n}})\) rounds. Random Struct Algorithms 10(3):385–405MathSciNetCrossRefGoogle Scholar
  11. 11.
    Grimmet GR, McDiarmid CJH (1975) On coloring random graphs. Math Proc Camb Philos Soc 77:313–324CrossRefGoogle Scholar
  12. 12.
    Halldorsson MM (1991) Frugal methods for the independent set and graph coloring problems. Ph.D. thesis, The State University of New Jersey, New Brunswick, New Jersey, October 1991Google Scholar
  13. 13.
    Jones MT, Plassmann PE (1993) A parallel graph coloring heuristic. SIAM J Sci Comput 14(3):654–669MathSciNetCrossRefGoogle Scholar
  14. 14.
    König D (1931) Graphen und Matrizen. Math Lapok 38:116–119MATHGoogle Scholar
  15. 15.
    Lovasz L (1975) Three short proofs in graph theory. J Comb Theory Ser B 19:269–271MathSciNetCrossRefGoogle Scholar
  16. 16.
    Luby M (1986) A simple parallel algorithm for the maximal independent set problem. SIAM J Comput 15(4):1036–1055MathSciNetCrossRefGoogle Scholar
  17. 17.
    Matula DW, Marble G, Isaacson JD (1972) Graph coloring algorithms. Academic Press, New YorkMATHGoogle Scholar
  18. 18.
    Nishizeki T, Terada O, Leven D (1983) Algorithms for edge-coloring of graphs. Tohoku University, Electrical Communications Department, Technical report, TRECIS 83001Google Scholar
  19. 19.
    Vizing VG (1964) On an estimate of the chromatic class of a p-graph. Diskret Anal 3:25–30 (in Russian)MathSciNetGoogle Scholar
  20. 20.
    Welsh DJA, Powell MB (1967) An upper bound for the chromatic number of a graph and its application to timetabling problems. Comput J 10:85–86CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.International Computer InstituteEge UniversityIzmirTurkey

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