Closed trail decompositions of some classes of regular graphs

Paulraja, P.; Kumar, S. Sampath

doi:10.1016/j.disc.2011.12.015

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Cited by 2 publications

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“…Further, a C p -decomposition, p a prime, of the graph K m × K n was used to find a C p -decomposition of K m • K n , see [25]. Moreover, a resolvable 2k-cycle decomposition of K m × K n and a decomposition of K m × K n into closed trails of length k have been studied in [33,34]. Besides that, Hamilton cycle decompositions of the graphs [8,[28][29][30][31]35].…”

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confidence: 99%

Decomposition of the tensor product of complete graphs into cycles of lengths 3 and 6

Paulraja¹,

Srimathi²

2021

Discuss. Math. Graph Theory

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By a C α 3 , C β 6-decomposition of a graph G, we mean a partition of the edge set of G into α cycles of length 3 and β cycles of length 6. In this paper, necessary and sufficient conditions for the existence of a C α 3 , C β 6decomposition of (K m × K n)(λ), where × denotes the tensor product of graphs and λ is the multiplicity of the edges, is obtained. In fact, we prove that for λ ≥ 1, m, n ≥ 3 and (m, n) = (3, 3), a C α 3 , C β 6-decomposition of (K m × K n)(λ) exists if and only if λ(m − 1)(n − 1) ≡ 0 (mod 2) and 3α + 6β = λm(m−1)n(n−1) 2 .

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