Zarankiewicz Numbers and Bipartite Ramsey Numbers
(ندگان)پدیدآور
Collins, Alex F.Riasanovsky, Alexander W. N.Wallace, John C.Radziszowski, Stanis law P.
نوع مدرک
TextResearch Paper
زبان مدرک
Englishچکیده
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
کلید واژگان
Zarankiewicz numberbipartite Ramsey number
شماره نشریه
1تاریخ نشر
2016-06-011395-03-12
ناشر
University of Tehranسازمان پدید آورنده
Rochester Institute of Technology, School of Mathematical Sciences, Rochester, NY 14623University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104, USA
Trinity College, Department of Mathematics, Hartford, CT 06106, USA
Rochester Institute of Technology, Department of Computer Science, Rochester, NY 14623
شاپا
2476-27762476-2784