@article{511e87a3e5124cd69f755846c375a584, title = "Embedding of cycles in twisted cubes with edge-pancyclic", abstract = "In this paper, we study the embedding of cycles in twisted cubes. It has been proven in the literature that, for any integer l, 4 ≤ l ≤ 2 n , a cycle of length l can be embedded with dilation 1 in an n-dimensional twisted cube, n ≥ 3. We obtain a stronger result of embedding of cycles with edge-pancyclic. We prove that, for any integer l, 4 ≤ l ≤ 2 n , and a given edge (x,y) in an n-dimensional twisted cube, n ≥ 3, a cycle C of length l can be embedded with dilation 1 in the n-dimensional twisted cube such that (x,y) is in C in the twisted cube. Based on the proof of the edge-pancyclicity of twisted cubes, we further provide an O(llog∈l+n 2+nl) algorithm to find a cycle C of length l that contains (u,v) in TQ n for any (u,v) E(TQ n ) and any integer l with 4 ≤ l ≤ 2 n. {\textcopyright} 2007 Springer Science+Business Media, LLC.", keywords = "Cycle, Dilation, Edge-pancyclicity, Embedding, Interconnection network, Twisted cube", author = "Jianxi Fan and Xiaohua Jia and Xiaola Lin", year = "2008", month = jul, doi = "10.1007/s00453-007-9024-7", language = "English", volume = "51", pages = "264--282", journal = "Algorithmica (New York)", issn = "0178-4617", publisher = "Springer", number = "3", }