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
Let be a power of an odd prime . We show that the vertices of every graph can be partitioned into classes such that the number of edges in any induced subgraph is divisible by , where , and if , then .In particular, it is shown that and .
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