# ICS 269, Winter 1996: Theory Seminar

## 23 February 1996:

Thrackles

Mike Dillencourt, ICS, UC Irvine

A thrackle is a graph that can be drawn in the plane so that
- its edges are represented by simple curves; and
- any two distinct edges either meet at a single common endpoint
or cross at exactly one point, interior to both curves.

Thirty years ago, Conway conjectured that an *n*-vertex
thrackle has at most *n* edges. Lovász, Pach and
Szegedy recently made major progress towards resolving this
conjecture, by proving that an *n*-vertex thrackle has at most
2*n* edges. In this talk, I will present their proof.