標題: Disjoint cycles in hypercubes with prescribed vertices in each cycle 作者: Lin, Cheng-KuanTan, Jimmy J. M.Hsu, Lih-HsingKung, Tzu-Liang資訊工程學系Department of Computer Science 關鍵字: Spanning cycle;Hamiltonian cycle;Cyclable;Hypercube;Graph 公開日期: 1-Dec-2013 摘要: A graph G is spanning r-cyclable of order t if for any r nonempty mutually disjoint vertex subsets A(1), A(2) ,..., A(r) of G with vertical bar A(1) boolean OR A(2) boolean OR ... boolean OR A(r)vertical bar <= t, there exist r disjoint cycles C-1, C-2,...,Cr of G such that C-1 boolean OR C-2 boolean OR ... C-r spans G, and C-t contains A(i) for every i. In this paper, we prove that the n-dimensional hypercube Q(n) is spanning 2-cyclable of order n - 1 for n >= 3. Moreover, Q(n) is spanning k-cyclable of order k if k <= n - 1 for n >= 2. The spanning r-cyclability of a graph G is the maximum integer t such that G is spanning r-cyclable of order k for k = r, r + 1,..., t but is not spanning r-cyclable of order t + 1. We also show that the spanning 2-cyclability of Q(n) is n - for n >= 3. (C) 2013 Elsevier B.V. All rights reserved. URI: http://dx.doi.org/10.1016/j.dam.2013.07.004http://hdl.handle.net/11536/23211 ISSN: 0166-218X DOI: 10.1016/j.dam.2013.07.004 期刊: DISCRETE APPLIED MATHEMATICS Volume: 161 Issue: 18 起始頁: 2992 結束頁: 3004 Appears in Collections: Articles

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