# 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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