The spanning cyclability of Cayley graphs generated by transposition trees

Embedding cycles into a network topology is crucial for the network simulation. In particular, embedding Hamiltonian cycles is a major requirement for designing good interconnection networks. A graph G is called k-spanning cyclable if, for any k distinct vertices v1, v2, ... , vk of G, there exist k cycles C1, C2, ... , Ck in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci. If k = 1, this is the classical Hamiltonian problem. In this paper, we focus on embedding spanning disjoint cycles in Cayley graphs Gamma n generated by transposition trees and show that Gamma n is k-spanning cyclable if k < n - 2 and n > 3. Moreover, the result is optimal with respect to the degree of Gamma n. (c) 2022 Elsevier B.V. All rights reserved.