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On zero-sum delta-systems and multiple copies of hypergraphs

✍ Scribed by Yair Caro

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
492 KB
Volume
15
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

We prove the following generalization of earlier results of Bialostocki and Dierker [3] and Caro [7].

Theorem. Let t ⩾ k ⩾ 2 be positive integers such that k | t, and let c :E(K) → ℤ~k~ be a mapping of all the r‐subsets of an rt + k −1 element set into the cyclic group of order k; then there are t pairwise disjoint r‐subsets e~1~, e~2~, …, e~t~ such that Σ c(e~i~) = 0. This theorem is further generalized to Δ‐systems. An application of this theorem and extension of the proof technique are combined to establish the currently best estimates of the zero‐sum Ramsey numbers R(t__G__, ℤ~t~).

📜 SIMILAR VOLUMES

Zero-sum delta-systems and multiple copi
Zero-sum delta-systems and multiple copies of graphs
✍ Caro, Yair; Provstgaard, Christian 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 268 KB 👁 1 views

A main result proved in this paper is the following. Theorem. Let G be a noncomplete graph on n vertices with degree sequence where R is the zero-sum Ramsey number.

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