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Apr 22, 2010 at 0:47 history edited Douglas S. Stones CC BY-SA 2.5
found an error and an easier proof
Apr 22, 2010 at 0:39 comment added Hooked The post above striped out the curly braces and my rep is to low to edit the comment - Please pretend that the exist around the 0,3 and 0,5 etc...
Apr 22, 2010 at 0:27 comment added Hooked This is what I get for editing a post right before I leave! I am quite mistaken that ${0,4}$ belongs to the set $C(5,2)$ and your parity argument seems quite valid. The tricky part to the problem comes from the fact that not every combination of ${a,b}$ can work at once. Consider $C(6,2)$ with possible values of ${0,3} {0,5} {1,4} {2,5}$. Not all $2^4$ combination are possible since a walk the has the 0 node touching both the 3 and 5 node can not possibly have the 2 node touching the 5 node. The question maybe better as which of these $2^4$ combination's are valid non-intersecting paths?
Apr 21, 2010 at 23:51 history edited Douglas S. Stones CC BY-SA 2.5
deleted 9 characters in body
Apr 21, 2010 at 23:45 history answered Douglas S. Stones CC BY-SA 2.5