Disjoint cycles in hypercubes with prescribed vertices in each cycle

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Title:	Disjoint cycles in hypercubes with prescribed vertices in each cycle
Authors:	Cheng-Kuan, L;Lin, Cheng-Kuan;Jimmy, J.M.T;Jimmy, J.M.Tan;Hs, Lih-Hsing;Hsu, Lih-Hsing;龔自良;KUNG, TZU-LIANG
Contributors:	資訊工程學系
Keywords:	Spanning cycle, Hamiltonian cycle, Cyclable, Hypercube, Graph
Date:	201308
Issue Date:	2013-10-29 09:41:05 (UTC+0)
Abstract:	A graph G is spanning r-cyclable of order t if for any r nonempty mutually disjoint vertex subsets A1,A2,…,Ar of G with \|A1∪A2∪⋯∪Ar\|≤t, there exist r disjoint cycles C1,C2,…,Cr of G such that C1∪C2∪⋯∪Cr spans G, and Ci contains Ai for every i. In this paper, we prove that the n-dimensional hypercube Qn is spanning 2-cyclable of order n−1 for n≥3. Moreover, Qn 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 Qn is n−1 for n≥3.
Relation:	DISCRETE APPLIED MATHEMATICS
Appears in Collections:	[Department of Computer Science and Information Engineering] Journal Artical

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