C7-Decompositions of the Tensor Product of Complete Graphs

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Abstract

In this paper we consider a decomposition of Km × Kn, where × denotes the tensor product of graphs, into cycles of length seven. We prove that for m, n ≥ 3, cycles of length seven decompose the graph Km × Kn if and only if (1) either m or n is odd and (2) 14 | m(m − 1)n(n − 1). The results of this paper together with the results of [Cp-Decompositions of some regular graphs, Discrete Math. 306 (2006) 429–451] and [C5-Decompositions of the tensor product of complete graphs, Australasian J. Combinatorics 37 (2007) 285–293], give necessary and sufficient conditions for the existence of a p-cycle decomposition, where p ≥ 5 is a prime number, of the graph Km × Kn.

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Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

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CiteScore 2018: 0.73

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Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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