The Tutte Polynomial - is a `crossing' the same as a `bridge'? 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.
 A: The Wikipedia page for the Tutte polynmomial 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.  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.
A: I don't have access to the cited paper but if the term bridge is used as in the answer of @Greg Kuperberg (edit: and it is) then other synonyms from graph theory are isthmus, cut-edge, and cut-arc. An important feature of such a bridge $e$ of a (possibly disconnected) graph $G$ is that if $F$ is any spanning forest of $G$, then $e$ must be an edge in $F$. Equivalently, $e$ is not contained in any cycle of $G$. If $G$ is planar then the dual edge $e^*$ in the dual graph $G^*$ is a loop (a cycle of length one).
More generally, one can study the Tutte polynomial of a matroid. In this context an element $e$ that is in every basis of a given matroid is called an isthmus or a coloop. 
