On the equitable k *-laceability of hypercubes

Chung-Haw Chang (), Chao-Ming Sun, Hua-Min Huang and Lih-Hsing Hsu
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Chung-Haw Chang: Ming Hsin University of Science and Technology
Chao-Ming Sun: Chinese Military Academy
Hua-Min Huang: National Central University
Lih-Hsing Hsu: Providence University

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 22, 349-364

Abstract: Abstract Let G be a finite undirected bipartite graph. Let u, v be two vertices of G from different partite sets. A collection of k internal vertex disjoint paths joining u to v is referred as a k-container C k (u,v). A k-container is a k *-container if it spans all vertices of G. We define G to be a k *-laceable graph if there is a k *-container joining any two vertices from different partite sets. A k *-container C k * (u,v)={P 1,…,P k } is equitable if ||V(P i )|−|V(P j )||≤2 for all 1≤i,j≤k. A graph is equitably k *-laceable if there is an equitable k *-container joining any two vertices in different partite sets. Let Q n be the n-dimensional hypercube. In this paper, we prove that the hypercube Q n is equitably k *-laceable for all k≤n−4 and n≥5.

Keywords: Hamiltonian; Hamiltonian laceable; Container; Hypercube (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-007-9047-7

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