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» Hamiltonian paths with prescribed edges in hypercubes
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DM
2007
100views more  DM 2007»
13 years 11 months ago
Hamiltonian paths with prescribed edges in hypercubes
Given a set P of at most 2n − 4 prescribed edges (n ≥ 5) and vertices u and v whose mutual distance is odd, the n-dimensional hypercube Qn contains a hamiltonian path between ...
Tomás Dvorák, Petr Gregor
ENDM
2007
70views more  ENDM 2007»
13 years 11 months ago
Hamiltonian fault-tolerance of hypercubes
Given a set F of faulty edges or faulty vertices in the hypercube Qn and a pair of vertices u, v, is there a hamiltonian cycle or a hamiltonian path between u and v in Qn −F? We...
Tomás Dvorák, Petr Gregor
IPL
2008
80views more  IPL 2008»
13 years 11 months ago
Path partitions of hypercubes
A path partition of a graph G is a set of vertex-disjoint paths that cover all vertices of G. Given a set P = {{ai, bi}}m i=1 of pairs of distinct vertices of the n-dimensional hy...
Petr Gregor, Tomás Dvorák