Zero-sum partition theorems for graphs - Y. Caro; I. Krasikov; Y. Roditty (International Journal of Mathematics and Mathematical Sciences)
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.