East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A REMARK ON CIRCULANT DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS BY GREGARIOUS CYCLES

  • Received : 2016.12.16
  • Accepted : 2016.12.26
  • Published : 2017.01.31
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Abstract

Let k, m and t be positive integers with $m{\geq}4$ and even. It is shown that $K_{km+1(2t)}$ has a decomposition into gregarious m-cycles. Also, it is shown that $K_{km(2t)}$ has a decomposition into gregarious m-cycles if ${\frac{(m-1)^2+3}{4m}}$ < k. In this article, we make a remark that the decompositions can be circulant in the sense that it is preserved by the cyclic permutation of the partite sets, and we will exhibit it by examples.

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References

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