Hamiltonicity of hypercubes with a constraint of required and faulty edges

Lih-Hsing Hsu, Shu-Chung Liu () and Yeong-Nan Yeh
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Lih-Hsing Hsu: Providence University
Shu-Chung Liu: China University of Technology
Yeong-Nan Yeh: Academia Sinica

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 10, 197-204

Abstract: Abstract Let R and F be two disjoint edge sets in an n-dimensional hypercube Q n . We give two constructing methods to build a Hamiltonian cycle or path that includes all the edges of R but excludes all of F. Besides, considering every vertex of Q n incident to at most n−2 edges of F, we show that a Hamiltonian cycle exists if (A) |R|+2|F|≤2n−3 when |R|≥2, or (B) |R|+2|F|≤4n−9 when |R|≤1. Both bounds are tight. The analogous property for Hamiltonian paths is also given.

Keywords: Hamiltonian cycles and paths; Edge-fault-tolerance; Required edge; Hypercubes (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-007-9059-3

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