A Distributed Algorithm to Find Hamiltonian Cycles in $\mathcal{G}(n, p)$ Random Graphs

2005 ◽  
pp. 63-74 ◽  
Author(s):  
Eythan Levy ◽  
Guy Louchard ◽  
Jordi Petit
Keyword(s):  
Random Graphs ◽  
Distributed Algorithm ◽  
Hamiltonian Cycles

scholarly journals DISTRIBUTED ALGORITHMS FOR BUILDING HAMILTONIAN CYCLES IN k-ARY n-CUBES AND HYPERCUBES WITH FAULTY LINKS

2007 ◽  
Vol 08 (03) ◽  
pp. 253-284 ◽  
Author(s):  
IAIN A. STEWART
Keyword(s):  
Distributed Algorithms ◽  
Distributed Algorithm ◽  
Hamiltonian Cycle ◽  
Sequential Algorithm ◽  
Hamiltonian Cycles ◽  
Cube Formula

We derive a sequential algorithm Find-Ham-Cycle with the following property. On input: k and n (specifying the k-ary n-cube [Formula: see text]); F, a set of at most 2n − 2 faulty links; and v , a node of [Formula: see text], the algorithm outputs nodes v + and v − such that if Find-Ham-Cycle is executed once for every node v of [Formula: see text] then the node v + (resp. v −) denotes the successor (resp. predecessor) node of v on a fixed Hamiltonian cycle in [Formula: see text] in which no link is in F. Moreover, the algorithm Find-Ham-Cycle runs in time polynomial in n and log k. We also obtain a similar algorithm for an n-dimensional hypercube with at most n − 2 faulty links. We use our algorithms to obtain distributed algorithms to embed Hamiltonian cycles k-ary n-cubes and hypercubes with faulty links; our hypercube algorithm improves on a recently-derived algorithm due to Leu and Kuo, and our k-ary n-cube algorithm is the first distributed algorithm for embedding a Hamiltonian cycle in a k-ary n-cube with faulty links.

scholarly journals On the existence of Hamiltonian cycles in a class of random graphs

1983 ◽  
Vol 45 (2-3) ◽  
pp. 301-305 ◽  
Author(s):  
T.I. Fenner ◽  
A.M. Frieze
Keyword(s):  
Random Graphs ◽  
Hamiltonian Cycles

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs
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