✦ LIBER ✦

On zero-sum Ramsey numbers— stars

✍ Scribed by Yair Caro

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 347 KB
Volume: 104
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90621-l

No coin nor oath required. For personal study only.

✦ Synopsis

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 raised by Bialostocfo and Dierker we prove that if k'f n then n+k-1 n=k=O(mod2), WI,~.G)=(~+~ otherwise.

📜 SIMILAR VOLUMES

Zero-Sum Ramsey Numbers modulo 3

✍ Heiko Harborth; Lothar Piepmeyer 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 184 KB

Simple proofs are given for three infinite classes of zero-sum Ramsey numbers modulo 3: r(K n , Z 3 )=n+3 for n#1, 4 (mod 9) and r(K n , Z 3 )=n+4 for n#0 (mod 9).

Binomial Coefficients and Zero-Sum Ramse

Binomial Coefficients and Zero-Sum Ramsey Numbers

✍ Yair Caro 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 307 KB

A counting argument is developed and divisibility properties of the binomial coefficients are combined to prove, among other results, that where K n , resp. K k n , is the complete, resp. complete k-uniform, hypergaph and R(K n , Z p ), R(K k n , Z 2 ) are the corresponding zero-sum Ramsey numbers.

On zero sum Ramsey numbers: Multiple cop

On zero sum Ramsey numbers: Multiple copies of a graph

✍ A. Bialostocki; P. Dierker 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 376 KB 👁 1 views

## Abstract As a consequence of our main result, a theorem of Schrijver and Seymour that determines the zero sum Ramsey numbers for the family of all __r__‐hypertrees on __m__ edges and a theorem of Bialostocki and Dierker that determines the zero sum Ramsey numbers for __r__‐hypermatchings are com

The characterization of zero-sum (mod 2)

The characterization of zero-sum (mod 2) bipartite Ramsey numbers

✍ Caro, Yair; Yuster, Raphael 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB

Let G be a bipartite graph, with k|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 article we give the first proof that determines B(G, Z 2 ) for all possib

On three zero-sum Ramsey-type problems

✍ Noga Alon; Yair Caro 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 821 KB

## Abstract For a graph __G__ whose number of edges is divisible by __k__, let __R__(__G,Z__~k~) denote the minimum integer __r__ such that for every function __f__: __E__(__K__~r~) ↦ __Z__~k~ there is a copy __G__^1^ of __G__ in __K__~r~ so that Σe∈__E__(__G__^1^) __f(e)__ = 0 (in __Z__~k~). We pr

Size Ramsey numbers involving stars

✍ R.J. Faudree; J. Sheehan 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 302 KB

We calculate some size Ramsey numbers involving stars. For example we prove that for t ~ k w2 ~md n sufficiently large the size Ramsey number r,, (K,,k All graphs in this paper are finite, simple and undirected. Let F, C and H be graphs. The number of vertices and edges of a graph F will be denoted