Zero-sum bipartite Ramsey numbers
نویسندگان
چکیده
منابع مشابه
Diagonal forms and zero-sum (mod 2) bipartite Ramsey numbers
Let G be a subgraph of a complete bipartite graph Kn,n. Let N(G) be a 0-1 incidence matrix with edges of Kn,n against images of G under the automorphism group of Kn,n. A diagonal form of N(G) is found for every G, and whether the row space of N(G) over Zp contains the vector of all 1’s is determined. This re-proves Caro and Yuster’s results on zero-sum bipartite Ramsey numbers [3], and provides...
متن کاملThe characterization of zero-sum (mod 2) bipartite Ramsey numbers
Let G be a bipartite graph, with k | e(G). The zero-sum bipartite Ramsey number B(G,Zk) is the smallest integer t such that in every Zk-coloring of the edges of Kt,t, there is a zero-sum mod k copy of G in Kt,t. In this paper we give the first proof which determines B(G,Z2) for all possible bipartite graphs G. In fact, we prove a much more general result from which B(G,Z2) can be deduced: Let G...
متن کاملZarankiewicz Numbers and Bipartite Ramsey Numbers
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...
متن کاملOn zero-sum Ramsey numbers - stars
Caro, Y., On zero-sum Ramsey numbers--stars, Discrete Mathematics 104 (1992) l-6. Let n 3 k 2 2 be positive integers, k ( n. Let H, be the cyclic group of order k. Denote by R(K,,,> Z,) the minimal integer t such that for every &-coloring of the edges of K,, (i.e., a function c : E(K,)+ hk), there is in K, a copy of K, n with the property that CeeE(k, ) c(e) = 0 (mod k). Answering a problem rai...
متن کاملBipartite rainbow Ramsey numbers
Let G and H be graphs. A graph with colored edges is said to be monochromatic if all its edges have the same color and rainbow if no two of its edges have the same color. Given two bipartite graphs G1 and G2, the bipartite rainbow ramsey number BRR(G1; G2) is the smallest integer N such that any coloring of the edges of KN;N with any number of colors contains a monochromatic copy of G1 or a rai...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1993
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1993.128379