The Tutte Polynomial - is a `crossing' the same as a `bridge'? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T17:04:56Z http://mathoverflow.net/feeds/question/54517 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54517/the-tutte-polynomial-is-a-crossing-the-same-as-a-bridge The Tutte Polynomial - is a `crossing' the same as a `bridge'? vivid-colours 2011-02-06T13:58:56Z 2011-02-06T14:16:40Z <p>Hey guys,</p> <p>The following paper uses the term `bridge' in their definition of the Tutte polynomial:</p> <p>Bennett Thompson, David J. Pearce, Craig Anslow, and Gary Haggard. Visualizing the computation tree of the tutte polynomial. In Proceedings of the 4th ACM sympo- sium on Software visualization, SoftVis ’08, pages 211–212, New York, NY, USA, 2008. ACM. Available from: <a href="http://doi.acm.org/10.1145/1409720.1409760" rel="nofollow">http://doi.acm.org/10.1145/1409720.1409760</a>, doi:http: //doi.acm.org/10.1145/1409720.1409760.</p> <p>However, the Wiki page and other papers use the term `crossing'.</p> <p>Are these the same thing or am I confusing them? What do you think?</p> <p>Thank you.</p> http://mathoverflow.net/questions/54517/the-tutte-polynomial-is-a-crossing-the-same-as-a-bridge/54519#54519 Answer by Greg Kuperberg for The Tutte Polynomial - is a `crossing' the same as a `bridge'? Greg Kuperberg 2011-02-06T14:16:28Z 2011-02-06T14:16:28Z <p>The Wikipedia page for the <a href="http://en.wikipedia.org/wiki/Tutte_polynomial" rel="nofollow">Tutte polynmomial</a> doesn't use the word crossing, it also uses the word bridge. In graph theory, a bridge of a connected graph is an edge that separates the graph into two components.</p> <p>However, there is a relation between the Tutte polynomial and the Jones and HOMFLY polynomials. More precisely, the HOMFLY polynomial <a href="http://www.jstor.org/pss/2047194" rel="nofollow">generalizes the Tutte polynomial for planar graph</a>. A knot diagram has crossings, which means points where two arcs of the knot cross. A knot diagram also has bridges; a bridge is a maximal sequence of over-crossings along an arc of the diagram. So there is a little bit of collision of terminology, because crossings aren't bridges and because bridges for knots aren't the same as bridges for graphs.</p>