Complete Cycle Embedding in Crossed Cubes with Two-Disjoint-Cycle-Cover Pancyclicity

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Title:	Complete Cycle Embedding in Crossed Cubes with Two-Disjoint-Cycle-Cover Pancyclicity
Authors:	KUNG, Tzu-Liang CHEN, Hon-Chan
Contributors:	圖書館
Keywords:	pancyclic vertex-disjoint cycles disjoint-cycle cover cycle embedding crossed cube
Date:	2015
Issue Date:	2016-10-18 16:12:42 (UTC+8)
Abstract:	A graph G is two-disjoint-cycle-cover r-pancyclic if for any integer l satisfying r≤l≤\|V(G)\|-r, there exist two vertex-disjoint cycles C1 and C2 in G such that the lengths of C1 and C2 are \|V(G)\|-l and l, respectively, where \|V(G)\| denotes the total number of vertices in G. In particular, the graph G is two-disjoint-cycle-cover vertex r-pancyclic if for any two distinct vertices u and v of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains u, (ii) C2 contains v, and (iii) the lengths of C1 and C2 are \|V(G)\|-l and l, respectively, for any integer l satisfying r≤l≤\|V(G)\|-r. Moreover, G is two-disjoint-cycle-cover edge r-pancyclic if for any two vertex-disjoint edges (u,v) and (x,y) of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains (u,v), (ii) C2 contains (x,y), and (iii) the lengths of C1 and C2 are \|V(G)\|-l and l, respectively, for any integer l satisfying r≤l≤\|V(G)\|-r. In this paper, we first give Dirac-type sufficient conditions for general graphs to be two-disjoint-cycle-cover vertex/edge 3-pancyclic, and we also prove that the n-dimensional crossed cube CQn is two-disjoint-cycle-cover 4-pancyclic for n≥3, vertex 4-pancyclic for n≥5, and edge 6-pancyclic for n≥5.
Relation:	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, issue 12, pp. 2670-2676
Appears in Collections:	[Department of Information Management] 【資訊管理系】期刊論文

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