Fault-Free Pairwise Independent Hamiltonian Paths on Faulty Hypercubes

Author(s):  
Sun-Yuan Hsieh
Keyword(s):  
2008 ◽  
Vol 107 (5) ◽  
pp. 171-176 ◽  
Author(s):  
Chung-Meng Lee ◽  
Jimmy J.M. Tan ◽  
Lih-Hsing Hsu

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Dave Witte Morris

We construct an infinite family {Cay→(Gi;ai;bi)} of connected, 2-generated Cayley digraphs that do not have hamiltonian paths, such that the orders of the generators ai and bi are unbounded. We also prove that if G is any finite group with |[G,G]|≤3, then every connected Cayley digraph on G has a hamiltonian path (but the conclusion does not always hold when |[G,G]|=4 or 5).


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