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Date: Fri, 24 Apr 98 09:38:06 EDT
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From: Dan Hoey <Hoey@aic.nrl.navy.mil>
To: cube-lovers@ai.mit.edu
Cc: whuang@ugcs.caltech.edu
Subject: Re: Hamiltonian circuits on the cube

I wrote:
> I actually generated all the continuous chiral isopaths, and the
> following is the other extreme--the only one with nine disjoint paths.

Which was bogus.  I actually generated only the continuous chiral
isopaths in which no circuit lies entirely on one face.  That's fine
for the Hamiltonian circuit problem, but for the maximum number of
disjoint circuits we probably want the 14-circuit pattern

                        +-@-+-@-+-@-+---+---+---+
                        |@@   @@@@@ | @@@@@   @@|
                        +   +   +   + @ + @ + @ +
                        |@@   @@@@@ | @@@@@   @@|
                        + @ + @ + @ +   +   +   +
                        |@@   @@@@@ | @@@@@   @@|
            +-@-+-@-+-@-+---+---+---+-@-+-@-+-@-+
            |@@   @@@@@ | @@@@@   @@|
            +   +   +   + @ + @ + @ +
            |@@   @@@@@ | @@@@@   @@|
            + @ + @ + @ +   +   +   +
            |@@   @@@@@ | @@@@@   @@|
+-@-+-@-+-@-+---+---+---+-@-+-@-+-@-+
|@@   @@@@@ | @@@@@   @@|
+   +   +   + @ + @ + @ +
|@@   @@@@@ | @@@@@   @@|
+ @ + @ + @ +   +   +   +
|@@   @@@@@ | @@@@@   @@|
+---+---+---+-@-+-@-+-@-+

which should be familiar to Tartan fans.

Dan
Hoey@AIC.NRL.Navy.Mil