Hi 


A circle graph is defined as the intersection graph of a set of chords of a circle.


I'm interested in any information which might help to enumerate connected circle graphs.


Thanks


Andy



Enumerating Connected Circle Graphs
You can find a table enumerating the connected circle graphs up to $n=12$ at this
Univ. Bergen link: [Database of Circle Graphs](http://www.ii.uib.no/~larsed/circle/). For example, there are 892,278,076 connected
circle graphs on 12 vertices. The paper that explains how the enumeration was
computed is "Interlace Polynomials: Enumeration, Unimodality, and Connections to Codes"
by
Lars Eirik Danielsen and Matthew G. Parker (2009); [arXiv:0804.2576v2 [math.CO]](http://arxiv.org/abs/0804.2576).


