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Embedding of Cycles in Twisted Cubes with Edge-Pancyclic

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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≤2n, 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≤2n, 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≤2n.

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Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong, Hong Kong

    Jianxi Fan & Xiaohua Jia

  2. College of Information Science and Technology, Sun Yat-sen University, Guangzhou, China

    Xiaola Lin

  3. College of Information Engineering, Qingdao University, Qingdao, 266071, China

    Jianxi Fan

Authors
  1. Jianxi Fan
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  2. Xiaohua Jia
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  3. Xiaola Lin
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Correspondence to Jianxi Fan.

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Fan, J., Jia, X. & Lin, X. Embedding of Cycles in Twisted Cubes with Edge-Pancyclic. Algorithmica 51, 264–282 (2008). https://doi.org/10.1007/s00453-007-9024-7

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  • DOI: https://doi.org/10.1007/s00453-007-9024-7

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