On a Problem in Graph Theory

P. Erdös

doi:10.2307/3613396

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Suppose there are n towns every pair of which are connected by a single one-way road (roads meet only at towns). Is it possible to choose the direction of the traffic on all the roads so that if any two towns are named there is always a third from which the two named can be reached directly by road?

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Wallis, W. D. 1970. ON EXTREME TOURNAMENTS. Annals of the New York Academy of Sciences, Vol. 175, Issue. 1 The Impac of, p. 403.

Wallis, W. D. 1970. ON EXTREME TOURNAMENTS. Annals of the New York Academy of Sciences, Vol. 175, Issue. 1, p. 403.

Graham, R. L. and Spencer, J. H. 1971. A Constructive Solution to a Tournament Problem. Canadian Mathematical Bulletin, Vol. 14, Issue. 1, p. 45.

Aanderaa, Stål and Goldfarb, Warren D. 1974. The finite controllability of the Maslov case. Journal of Symbolic Logic, Vol. 39, Issue. 3, p. 509.

Eplett, W. J. R. 1977. Counting the circuits in a graph. The Mathematical Gazette, Vol. 61, Issue. 416, p. 126.

Spencer, Joel 1985. Probabilistic methods. Graphs and Combinatorics, Vol. 1, Issue. 1, p. 357.

Spencer, Joel 1986. Combinatorics by Coin Flipping. The College Mathematics Journal, Vol. 17, Issue. 5, p. 407.

Israeli, Amos and Li, Ming 1987. Bounded time-stamps. p. 371.

Megiddo, Nimrod and Vishkin, Uzi 1988. On finding a minimum dominating set in a tournament. Theoretical Computer Science, Vol. 61, Issue. 2-3, p. 307.

Erdös, P. Faudree, R. Gyárfás, A. and Schelp, R. H. 1989. Domination in colored complete graphs. Journal of Graph Theory, Vol. 13, Issue. 6, p. 713.

Alon, Noga 1989. Geometric Aspects of Functional Analysis. Vol. 1376, Issue. , p. 186.

Chung, F. R. K. and Graham, R. L. 1991. Quasi‐random tournaments. Journal of Graph Theory, Vol. 15, Issue. 2, p. 173.

Li, M. and Vitanyi, P.M.B. 1991. Combinatorics and Kolmogorov complexity. p. 154.

Israeli, Amos and Li, Ming 1993. Bounded time-stamps. Distributed Computing, Vol. 6, Issue. 4, p. 205.

Li, Ming and Vitányi, Paul M.B 1994. Kolmogorov complexity arguments in combinatorics. Journal of Combinatorial Theory, Series A, Vol. 66, Issue. 2, p. 226.

Simonovits, Miklós 1997. The Mathematics of Paul Erdös II. Vol. 14, Issue. , p. 148.

Tyszkiewicz, Jerzy 2000. A Simple Construction for Tournaments With Every k Players Beaten by a Single Player. The American Mathematical Monthly, Vol. 107, Issue. 1, p. 53.

Gutin, Gregory Koh, Khee Meng Tay, Eng Guan and Yeo, Anders 2004. On the number of quasi‐kernels in digraphs. Journal of Graph Theory, Vol. 46, Issue. 1, p. 48.

Bonato, Anthony and Cameron, Kathie 2006. On an adjacency property of almost all tournaments. Discrete Mathematics, Vol. 306, Issue. 19-20, p. 2327.

Alon, Noga Brightwell, Graham Kierstead, H.A. Kostochka, A.V. and Winkler, Peter 2006. Dominating sets in k-majority tournaments. Journal of Combinatorial Theory, Series B, Vol. 96, Issue. 3, p. 374.

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On a Problem in Graph Theory

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