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On the equitable k *-laceability of hypercubes

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chung-Haw Chang & Chao-Ming Sun & Hua-Min Huang & Lih-Hsing Hsu, 2007. "On the equitable k *-laceability of hypercubes," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 349-364, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9047-7
    DOI: 10.1007/s10878-007-9047-7
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