MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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:, doi:http: //

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.

share|cite|improve this question
up vote 3 down vote accepted

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.

share|cite|improve this answer
And of course Tutte used "bridge" with a completely different meaning. The joys of terminology. – Chris Godsil Feb 6 '11 at 15:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.