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Collins, Alex F., Riasanovsky, Alexander W. N., Wallace, John C., Radziszowski, Stanis law P.. (1395). Zarankiewicz Numbers and Bipartite Ramsey Numbers. , 47(1), 63-78. doi: 10.22059/jac.2016.7943
Alex F. Collins; Alexander W. N. Riasanovsky; John C. Wallace; Stanis law P. Radziszowski. "Zarankiewicz Numbers and Bipartite Ramsey Numbers". , 47, 1, 1395, 63-78. doi: 10.22059/jac.2016.7943
Collins, Alex F., Riasanovsky, Alexander W. N., Wallace, John C., Radziszowski, Stanis law P.. (1395). 'Zarankiewicz Numbers and Bipartite Ramsey Numbers', , 47(1), pp. 63-78. doi: 10.22059/jac.2016.7943
Collins, Alex F., Riasanovsky, Alexander W. N., Wallace, John C., Radziszowski, Stanis law P.. Zarankiewicz Numbers and Bipartite Ramsey Numbers. , 1395; 47(1): 63-78. doi: 10.22059/jac.2016.7943

Zarankiewicz Numbers and Bipartite Ramsey Numbers

Journal of Algorithms and Computation
مقاله 7، دوره 47، شماره 1، شهریور 2016، صفحه 63-78    اصل مقاله (364.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jac.2016.7943
نویسندگان
Alex F. Collins* 1؛ Alexander W. N. Riasanovsky2؛ John C. Wallace3؛ Stanis law P. Radziszowski4
1Rochester Institute of Technology, School of Mathematical Sciences, Rochester, NY 14623
2University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104, USA
3Trinity College, Department of Mathematics, Hartford, CT 06106, USA
4Rochester Institute of Technology, Department of Computer Science, Rochester, NY 14623
چکیده
The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.
In this work, we design and exploit a computational method for bounding and computing Zarankiewicz numbers. Using it, we obtain several new values and bounds on z(b; s) for 3≤s≤6. Our approach and new knowledge about z(b; s) permit us to improve some of the results on bipartite Ramsey numbers obtained by
کلیدواژه‌ها
Zarankiewicz number؛ bipartite Ramsey number
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