The Two-Disjoint-Path-Coverable Problem of Crossed Cubes

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Title:	The Two-Disjoint-Path-Coverable Problem of Crossed Cubes
Authors:	Chen, Hon-Chan;Kung, Tzu-Liang;Hsu, Li-Yen
Contributors:	資訊工程學系
Keywords:	Hamiltonian, Disjoint path cover, Path length, Interconnection network, Crossed cube
Date:	2013-12
Issue Date:	2013-12-18 02:42:56 (UTC+0)
Abstract:	A graph G is 2-disjoint-path-coverable (2-DPC) if, for any four distinct vertices u, v, x, and y of G, there exist two vertex-disjoint paths P1 and P2 such that (i) P1 joins u and v, (ii) P2 joins x and y, and (iii) P1 ∪ P2 spans G. In this paper, we investigate the 2-DPC problem of the crossed cube with various path lengths. In particu-lar, we prove that the crossed cube can be spanned by two disjoint paths P1 of length l1 and P2 of length l2, where 2n–2 – 1 ? l1 ? 2n–1 – 1 and l2 = 2n – l1 – 2. This result im-proves on the previous one that the two disjoint paths are of equal length.
Relation:	2013全國計算機會議
Appears in Collections:	[Department of Computer Science and Information Engineering] Proceedings

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