Embedding mutually edge-disjoint cycles into locally twisted cubes

Abstract

The n-dimensional locally twisted cube LTQn, an important variation of the hypercube, can be denoted by LTQn=LTQn−10⊕LTQn−11=(LTQn−200⊕LTQn−201)⊕(LTQn−210⊕LTQn−211). In this paper, we prove that for any node x in LTQn, there are ⌊n2⌋ edge-disjoint cycles containing x such that each cycle has intersection with each LTQn−2αβ, where αβ∈{00,01,10,11} and n≥4. Since LTQn is n-regular and each node has degree 2 in each cycle, our result is optimal.