Hey guys,


The following paper uses the term `bridge' in their definition of the Tutte polynomial:


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: <http://doi.acm.org/10.1145/1409720.1409760>, doi:http: //doi.acm.org/10.1145/1409720.1409760.


However, the Wiki page and other papers use the term `crossing'.


Are these the same thing or am I confusing them? What do you think?


Thank you.



The Tutte Polynomial - is a `crossing' the same as a `bridge'?
The Wikipedia page for the [Tutte polynmomial](http://en.wikipedia.org/wiki/Tutte_polynomial) 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.


However, there is a relation between the Tutte polynomial and the Jones and HOMFLY polynomials. More precisely, the HOMFLY polynomial [generalizes the Tutte polynomial for planar graph](http://www.jstor.org/pss/2047194). 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.


