On December 8, 2020, Hong Liu from University of Warwick presented a talk on his recent work with Richard Montgomery, answering the odd cycle problem of Erdős and Hajnal (1981). The title of his talk is “A solution to Erdős and Hajnal’s odd cycle problem“.

## Hong Liu (刘鸿), A solution to Erdős and Hajnal’s odd cycle problem

I will go over the history on the study of the set of cycle lengths of graphs with large average degree or chromatic number, and discuss recent work with Richard Montgomery on this topic. In particular, we will see the divergence of harmonic sum of odd cycle lengths in graphs with large chromatic number and the appearance of cycle lengths in very sparse sequences (such as powers of 2). The methods developed in this work allows also us to embed equally divided clique subdivisions, which was conjectured by Thomassen.

## Hong Liu (刘鸿), Cycles and trees in graphs (8/8)

This lecture series covers several different techniques on embedding paths/trees/cycles in (pseudo)random graphs/expanders as (induced) subgraphs.

## Hong Liu (刘鸿), Cycles and trees in graphs (7/8)

This lecture series covers several different techniques on embedding paths/trees/cycles in (pseudo)random graphs/expanders as (induced) subgraphs.

## Hong Liu (刘鸿), Cycles and trees in graphs (6/8)

This lecture series covers several different techniques on embedding paths/trees/cycles in (pseudo)random graphs/expanders as (induced) subgraphs.