most recent 30 from http://mathoverflow.net 2013-05-22T14:35:11Z http://mathoverflow.net/feeds/user/9717 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81639/does-there-exist-infinitely-many-prime-knots/81641#81641 Jana Archibald 2011-11-22T19:29:07Z 2011-11-22T19:29:07Z

<p>Yes there are infinitely many prime knots. </p> <p>Not a "proof from the book", but all (p,2) torus knots for p prime are prime, and they have different Alexander polynomials. </p>

http://mathoverflow.net/questions/40887/polygons-arising-from-knot-diagrams/40966#40966 Jana Archibald 2010-10-03T22:36:05Z 2010-10-03T22:36:05Z

<p>Colin Adams, Reiko Shinjo and Kokoro Tanaka have a paper (http://arxiv.org/abs/0812.2558) that shows that for any knot you can find a diagram which has only regions with 2, 4 and 5 sides. </p>

http://mathoverflow.net/questions/76845/untangling-a-graph Jana Archibald 2011-09-30T13:12:59Z 2011-09-30T13:12:59Z

A no-brainer proof that crossing flips unknot knots, is imagining walking along your knot. The first time you see a crossing change it (if necessary) so that you walk along the top strand. Once you have traversed the knot it will be unknotted. As to your actual question, I am unsure what you mean. Are you thinking of working with a planar 4-valent graph, and allowing planar projections of the Reidemeister moves?