Results 1 to 3 of about 3 (3)

A linear upper bound in zero‐sum Ramsey theory

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 609-612, 1994., 1994
Let n, r and k be positive integers such that . There exists a constant c(k, r) such that for fixed k and r and for every group A of order k where is the zero‐sum Ramsey number introduced by Bialostocki and Dierker [1], and is the complete r‐uniform hypergraph on n‐vertices.
Yair Caro
wiley   +1 more source

Zero‐sum partition theorems for graphs

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 697-702, 1994., 1993
Let q = pn be a power of an odd prime p. We show that the vertices of every graph G can be partitioned into t(q) classes such that the number of edges in any induced subgraph 〈Vi〉 is divisible by q, where , and if q = 2n, then t(q) = 2q − 1. In particular, it is shown that t(3) = 3 and 4 ≤ t(5) ≤ 5.
Y. Caro, I. Krasikov, Y. Roditty
wiley   +1 more source

A monotone path in an edge‐ordered graph

International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 2, Page 315-320, 1987., 1986
An edge‐ordered graph is an ordered pair (G, f), where G is a graph and f is a bijective function, f : E(G) → {1, 2, …, |E(G)|}. A monotone path of length k in (G, f) is a simple path Pk+1 : v1v2 … vk+1 in G such that either f({vi, vi+1}) < f({vi+1, vi+2}) or f({vi, vi+1}) > f({vi+1, vi}) for i = 1, 2, …, k − 1.
A. Bialostocki, Y. Roditty
wiley   +1 more source