A Complete Characterization of the Zero-Sum (mod 2) Ramsey Numbers

نویسنده

  • Yair Caro
چکیده

THEOREM. Let G be a graph on n vertices and an euen number of edges. Then the zero-sum (mod 2) Ramsey numbers are given by {i +2 R(G, ~2) = + 1 +t ifG=Kn, n =0,1(mod4) if all the degrees in G are odd otherwise. 0 (mod 2) This settles several problems raised mainly by Noga Alon, Arie Bialostocki, and Yehuda Roditty.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

The Characterization of Zero - Sum ( mod 2 ) Bipartite

Let G be a bipartite graph, with k j e(G). The zero-sum bipartite Ramsey number B(G; Z k) is the smallest integer t such that in every Z k-coloring of the edges of K t;t , there is a zero-sum mod k copy of G in K t;t. In this paper we give the rst proof which determines B(G; Z 2) for all possible bipartite graphs G. In fact, we prove a much more general result from which B(G; Z 2) can be deduce...

متن کامل

On 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 کامل

The 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 کامل

Special Numbers in the Ring Zn

In a recent article, Nowicki introduced the concept of a special number. Specifically, an integer d is called special if for every integer m there exist solutions in non-zero integers a, b, c to the equation a + b − dc = m. In this article we investigate pairs of integers (n, d), with n ≥ 2, such that for every integer m there exist units a, b, and c in Zn satisfying m ≡ a 2 + b − dc (mod n). B...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 68  شماره 

صفحات  -

تاریخ انتشار 1994