International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1994 / Article

Open Access

Volume 17 |Article ID 250807 |

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.

Zero-sum partition theorems for graphs

Received13 Nov 1992
Revised02 Feb 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 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.

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