Probabilistic analysis of graph colouring algorithms

  • A. Marchetti-Spaccamela
  • M. Talamo
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 159)


In this paper we analyze algorithms for the graph colouring problem from a probabilistic point of view. Furthermore we show that the chromatic number of a graph converges to n log 1/q / 2 log n almost surely.


Greedy Algorithm Probabilistic Analysis Random Graph Travelling Salesman Problem Chromatic Number 


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  1. [1]
    B. BOLLOBAS, P. ERDÖS: Cliques in random graphs. Math. Proc. Camb. Phil. Soc., vol. 80, (1976).Google Scholar
  2. [2]
    P. ERDÖS, A. RENYI: On random graphs 1. Publ. Math., vol. 6, (1959).Google Scholar
  3. [3]
    M.R. GAREY, D.S. JOHNSON: The complexity of near-optimal graph colouring. J. ACM, vol. 33, n. 1, pp. 43–46 (1976).CrossRefGoogle Scholar
  4. [4]
    M.R. GAREY, D.S. JOHNSON: Computers and intractability: a guide to the theory of NP-completeness. Freeman San Francisco (1978).Google Scholar
  5. [5]
    G.R. GRIMETT, C.J.H. Mc DIARMID: On colouring random graphs. Math. Proc. Camb. Phil. Soc., vol. 77, pp. 313–324, (1975).Google Scholar
  6. [6]
    R.M. KAPP: The probabilistic analysis of some combinatorial search algorithms. In J.F. Traub (ed.), Algorithms and complexity J.F. Traud, Academic Press (1976).Google Scholar
  7. [7]
    E.L. LAWLER: A note on the complexity of the chromatic number. Inf. Proc. Let. (1976).Google Scholar
  8. [8]
    C.J.H. Mc DIARMID: Determining the chromatic number of a graph. SIAM J. on Comp. (1981).Google Scholar
  9. [9]
    M. TALAMO: Analisi probabilistica della complessità di algoritmi di colorazione. Thesis Università di Roma (1981).Google Scholar
  10. [10]
    M. TALAMO: A probabilistic of some greedy algorithms. Technical Report R.12 Istituto di Automatica, Università di Roma (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • A. Marchetti-Spaccamela
    • 1
  • M. Talamo
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di RomaRomaItalia

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