Zero-sum partition theorems for graphs

Y. Caro, I. Krasikov and Y. Roditty

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-6

Abstract:

Let q = p n 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 = 1 t ( q ) V i such that the number of edges in any induced subgraph 〈 V i 〉 is divisible by q , where t ( q ) ≤ 3 2 ( q − 1 ) − ( 2 ( q − 1 ) − 1 ) 1 2 4 + 9 8 , and if q = 2 n , then t ( q ) = 2 q − 1 .

In particular, it is shown that t ( 3 ) = 3 and 4 ≤ t ( 5 ) ≤ 5 .

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:250807

DOI: 10.1155/S0161171294000992

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