✦ LIBER ✦

Zero-Sum Ramsey Numbers modulo 3

✍ Scribed by Heiko Harborth; Lothar Piepmeyer

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 184 KB
Volume: 75
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0068

No coin nor oath required. For personal study only.

✦ Synopsis

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).

📜 SIMILAR VOLUMES

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.

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 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 Number of k-Sums Modulo k

✍ Béla Bollobás; Imre Leader 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 110 KB

Upper bounds for ramsey numbers R(3, 3,

Upper bounds for ramsey numbers R(3, 3, ?, 3) and Schur numbers

✍ Wan, Honghui 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 81 KB 👁 2 views

In this paper we show that for n ≥ 4, R(3, 3, . . . , 3) < n!( e-e -1 + 3 2 ) + 1. Consequently, a new bound for Schur numbers is also given. Also, for even n ≥ 6, the Schur number S n is bounded by S n < n!( e-e -1 + 3 2 ) -n + 2.

On ramsey-tuŕan numbers for 3-graphs

✍ A. F. Sidorenko 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 255 KB

## Abstract For every __r__‐graph __G__ let π(__G__) be the minimal real number ϵ such that for every ϵ < 0 and __n__ ϵ __n__~0~(λ, __G__) every __R__‐graph __H__ with __n__ vertices and more than (π + ϵ)(nr) edges contains a copy of __G__. The real number λ(__G__) is defined in the same way, addin