# Model Theory Seminar

### School of Mathematics, University of Leeds

This week's seminar will be in Roger Stevens Lecture Theatre 7 and will be on Tuesday 4th March at 2pm. We will meet before the seminar at about 1.40pm in the common room for tea and coffee.

The seminar is organised by Will Anscombe.

### Spring Term 2014

Week 8, Tuesday 4th March
Andrés Aranda López
The line graph of the universal homogeneous triangle-free graph $H_{3}$

I will give arguments proving an easy characterisation of line graphs of triangle-free graphs, prove that the automorphism group of $H_{3}$ does not act primitively on the set of edges of $H_{3}$ and that if we consider the equivalence classes of an invariant equivalence relation on the edges of $H_{3}$ as sets of vertices, then the intersection graph of these sets is again $H_{3}$. Finally, I will propose a finite ternary relational language in which I think the theory of the line graph of $H_{3}$ eliminates quantifiers.