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Deterministic Graph Games and a Probabilistic Intuition

Published online by Cambridge University Press:  12 September 2008

József Beck
Affiliation:
Department of Mathematics, Rutgers University, Busch Campus, Hill Center, New Brunswick, New Jersey 08903U.S.A. e-mail: jbeck@aramis.rutgers.edu

Abstract

There is a close relationship between biased graph games and random graph processes. In this paper, we develop the analogy and give further interesting instances.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Beck, J. (1981) Van der Waerden and Ramsey type games. Combinatorica 2 103116.CrossRefGoogle Scholar
[2]Beck, J. (1982) Remarks on positional games – Part I. Ada Math. Acad. Sci. Hungarica 40 6571.CrossRefGoogle Scholar
[3]Beck, J. (1985) Random graphs and positional games on the complete graph. Annals of Discrete Math. 28 713.Google Scholar
[4]Bollobás, B. (1982) Long paths in sparse random graphs. Combinatorica 2 223228.CrossRefGoogle Scholar
[5]Bollobás, B. (1985) Random Graphs, Academic Press, London 447ff.Google Scholar
[6]Chvátal, V. and Erdős, P. (1978) Biased positional games. Annals of Discrete Math. 2 221228.CrossRefGoogle Scholar
[7]Chvátal, V., Rödl, V., Szemerédi, E. and Trotter, W. T. (1983) The Ramsey number of a graph with bounded maximum degree. Journal of Combinatorial Theory Series B 34 239243.CrossRefGoogle Scholar
[8]Erdős, P. and Selfridge, J. (1973) On a combinatorial game. Journal of Combinatorial Theory Series A 14 298301.CrossRefGoogle Scholar
[9]Friedman, J. and Pippenger, N. (1987) Expanding graphs contain all small trees. Combinatorica 7 7176.CrossRefGoogle Scholar
[10]Komlós, J. and Szemerédi, E. (1973) Hamilton cycles in random graphs, Proc. of the Combinatorial Colloquium in Keszthely, Hungary, 10031010.Google Scholar
[11]Pósa, L. (1976) Hamilton circuits in random graphs. Discrete Math. 14 359–64.CrossRefGoogle Scholar
[12]Székely, L. A. (1981) On two concepts of discrepancy in a class of combinatorial games. Colloq. Math. Soc. János Bolyai 37 “Finite and Infinite Sets” Eger, Hungary. North-Holland, 679683.Google Scholar