Abstract
In an earlier paper [3] McDiarmid and I studied the chromatic number of a random graph on n vertices in which each edge is present with a prescribed probability p independently of the presence or absence of the other edges. Such random graphs differ from those which Erdös and Rényi considered in their paper [1] on the evolution of random graphs, for they were interested in graphs on n vertices with N(n) edges where N is a prescribed function and each N-subset of the set of possible edges occurs with equal probability. They noted that there is no essential difference between the two approaches.
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References
P. Erdös, A. Rényi: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5A (1960), 17–61.
E. N. Gilbert: Enumeration of labelled graphs. Can. J. Math. 8 (1956), 405–411.
G. R. Grimmett, C. J. H. McDiarmid: On colouring random graphs. Math. Proc. Camb. Phil. Soc. 77 (1975), 313–324.
W. T. Tutte: On dichromatic polynomials. J. Comb. Th. 2 (1967), 301–320.
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Grimmett, G. (1977). Random Graph Theorems. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_21
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DOI: https://doi.org/10.1007/978-94-010-9910-3_21
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