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Journal of the Ramanujan Mathematical Society

Volume 36, Issue 4, December 2021  pp. 283–290.

Disjoint cycles through prescribed vertices in multidimensional tori

Authors:  Amruta Shinde and Y. M. Borse
Author institution:Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, India

Summary:  For a positive integer r, a graph G is spanning r-cyclable if for any given set F of r vertices, there exists r vertex-disjoint cycles that together span G and each cycle contains exactly one vertex from F. It is known that the hypercube Q{n} and its variation, the crossed cube, are spanning r-cyclable for 1 ≤ r ≤ n-1. We prove that every n-dimensional torus, different from C{3} Box C{3}, is spanning r-cyclable for 1 ≤ r ≤ 2n-1.

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