**Discrete Mathematics and Optimization Seminar**

**BABAK FARZAD**

* University of Toronto*

Monday September 20th at 4.30pm

* Burnside 1205*

**Title. *** Choosability of Planar Graphs without Cycles of Specific Lengths.*

**Abstract. **
An *L*-colouring of a graph *G* is a vertex colouring
in which every vertex gets a colour from a list *L(v)* of allowed colours.

*G* is called *l*-choosable if *G* is *L*-colourable for all
possible assignments *L* in which all lists *L(v)* have *l*-colours.

Let *k* be an integer, *3<= k <=6*. Other known results imply that
if *G* is a planar graph with no cycle
of length *k*, then *G* is *4*-choosable.

We use the discharging method to prove the conjecture that if *G* is a
planar graph without *7*-cycles, then *G* is *4*-choosable.