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From: Yann David on 28 Feb 2010 10:14
Here is a relatively simple planar counterexample.


+-----------------------+ +---------------------------+
| +---------------+ | | +---------------+ |
| | | | | | | |
a---b---c---d---e---f---g---h---i---j---k---l---m---n---o---p
| | | | | | | |
| | +---------------+ | | +-----------+
| +---------------------------+ |
+-----------------------------------+


This gallery was found by a computer program that builds random planar
galleries and then looks for a Hamiltonian circuit.
It didn't find any with no feet overlaps and less than 8 arches, but
when feet overlaps are allowed, 5 arches suffice:


+-------------------+
| +-----------+ |
| | | |
a---b---c---d---e---f---g---h---i
| | | | | |
| | +-----------+ | |
| +-------------------+ |
+---------------------------+



Cheers,

Yann David

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