The super laceability of the hypercubes

Authors:
Chung-Haw Chang;Cheng-Kuan Lin;Hua-Min Huang;Lih-Hsing Hsu
Affiliations:
Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, ROC;Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, ROC;Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, ROC;Department of Information Engineering, Ta Hwa Institute of Technology, Hsinchu, Taiwan 30740, ROC and Department of Computer and Information Science, National Chiao Tung University, Hsinchu, 300, ...
Venue:
Information Processing Letters
Year:
2004

Citing 3
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Abstract

A k-container C(u,v) of a graph G is a set of k disjoint paths joining u to v. A k-container C(u, v) is a k*-container if every vertex of G is incident with a path in C(u,v). A bipartite graph G is k*-laceable if there exists a k*-container between any two vertices u, v from different partite set of G. A bipartite graph G with connectivity k is super laceable if it is i*-laceable for all i ≤ k. A bipartite graph G with connectivity k is f-edge fault-tolerant super laceable if G - F is i*-laceable for any 1 ≤ i ≤ k-f and for any edge subset F with |F|=f k-1. In this paper, we prove that the hypercube graph Qr is super laceable. Moreover, Qr is f-edge fault-tolerant super laceable for any f ≤ r - 2.