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Electronic Colloquium on Computational Complexity

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Reports tagged with Hamiltonian circuits:
TR95-047 | 5th October 1995
Martin Loebbing, Ingo Wegener

The Number of Knight's Tours Equals 33,439,123,484,294 -- Counting with Binary Decision Diagrams

An increasing number of results in graph theory, combinatorics and
theoretical computer science is obtained with the help of computers,
e.g. the proof of the Four Colours Theorem or the computation of
certain Ramsey numbers. Binary decision diagrams, known as tools in
hardware verification ... more >>>

TR07-063 | 2nd July 2007
Tomas Feder, Carlos Subi

Nearly Tight Bounds on the Number of Hamiltonian Circuits of the Hypercube and Generalizations

We conjecture that for every perfect matching $M$ of the $d$-dimensional
$n$-vertex hypercube, $d\geq 2$, there exists a second perfect matching $M'$
such that the union of $M$ and $M'$ forms a Hamiltonian circuit of the
$d$-dimensional hypercube. We prove this conjecture in the case where there are
two dimensions ... more >>>

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