A fault-free Hamiltonian cycle passing through prescribed edges in a hypercube with faulty edges

In this paper, we consider the problem of a fault-free Hamiltonian cycle passing through prescribed edges in an n-dimensional hypercube Q"n with some faulty edges. We obtain the following result: Let n>=2, [email protected]?E(Q"n), E"[email protected]?E(Q"n)\F with 1=<|E"0|=<2n-3, |F|

[1]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[2]  Abhijit Sengupta.  On Ring Embedding in Hypercubes with Faulty Nodes and Links , 1998, Inf. Process. Lett..

[3]  Jimmy J. M. Tan,et al.  Edge-bipancyclicity of conditional faulty hypercubes , 2007, Inf. Process. Lett..

[4]  Xie-Bin Chen,et al.  Cycles passing through prescribed edges in a hypercube with some faulty edges , 2007, Inf. Process. Lett..

[5]  Ming-Syan Chen,et al.  Processor Allocation in an N-Cube Multiprocessor Using Gray Codes , 1987, IEEE Transactions on Computers.

[6]  Chang-Hsiung Tsai.  Linear array and ring embeddings in conditional faulty hypercubes , 2004, Theor. Comput. Sci..

[7]  F. Harary,et al.  A survey of the theory of hypercube graphs , 1988 .

[8]  Tomás Dvorák,et al.  Hamiltonian Cycles with Prescribed Edges in Hypercubes , 2005, SIAM J. Discret. Math..

[9]  Jimmy J. M. Tan,et al.  Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes , 2003, Inf. Process. Lett..

[10]  I. Havel.  On Hamiltonian circuits and spanning trees of hypercubes , 1984 .

[11]  Chang-Hsiung Tsai,et al.  Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes , 2007, Inf. Sci..

[12]  Mee Yee Chan,et al.  On the Existence of Hamiltonian Circuits in Faulty Hypercubes , 1991, SIAM J. Discret. Math..

[13]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[14]  Frank Thomson Leighton.  Introduction to parallel algorithms and architectures: arrays , 1992 .

[15]  Jun-Ming Xu,et al.  Edge-fault-tolerant edge-bipancyclicity of hypercubes , 2005, Inf. Process. Lett..