International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 697-702
doi:10.1155/S0161171294000992
Zero-sum partition theorems for graphs
Y. Caro1
, I. Krasikov2
and Y. Roditty2
1Department of Mathematics, Haifa University, Oranim, Israel
2School of Mathematics, Tel-Aviv University, Ramat Aviv, Israel
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(q−1)−(2(q−1)−1)124+98, and if q=2n, then t(q)=2q−1.In particular, it is shown that t(3)=3 and 4≤t(5)≤5.