International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1994 / Article

Open Access

Volume 17 |Article ID 250807 | https://doi.org/10.1155/S0161171294000992

Y. Caro, I. Krasikov, Y. Roditty, "Zero-sum partition theorems for graphs", International Journal of Mathematics and Mathematical Sciences, vol. 17, Article ID 250807, 6 pages, 1994. https://doi.org/10.1155/S0161171294000992

Zero-sum partition theorems for graphs

Received13 Nov 1992
Revised02 Feb 1993

Abstract

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 V(G)=t=1t(q)Vi such that the number of edges in any induced subgraph Vi is divisible by q, where t(q)32(q1)(2(q1)1)124+98, and if q=2n, then t(q)=2q1.In particular, it is shown that t(3)=3 and 4t(5)5.

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views81
Downloads330
Citations

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.