Re: [math-fun] Square (& other) chains and necklaces.

Dan Asimov wrote:

Nice example! Now suppose every vertex is required to have finite valence. Then I think this slight modification of Mike's example will still serve as a graph where every {1,...,n} has a Hamiltonian path, but not {1,2,3,...}.

(This is a slight modification of Dan's graph.) 4--3--5--7--9---11--- | /| /| /| / | / ... |/ |/ |/ | / | / 1--2--6--8--10---12-- Now suppose we require Hamiltonian cycles for every {1,...,n}. Is there then a Hamiltonian path for N (there can't be a cycle). Suppose we require Hamiltonian cycles for every {a, ..., b} for a,b in Z? Can we then find a Hamiltonian path through Z? Dan (not that Dan, this Dan) Hoey@AIC.NRL.Navy.Mil