Coloring and girth

The study of graphs with high girth and high chromatic number had a profound influence on the history of Combinatrics and Graph Theory, and led to the development of sophisticated methods involving tools from topology, number theory, algebra and combinatorics. I will discuss the topic focusing on a recent new explicit construction of graphs (and hypergraphs) of high girth and high chromatic number, in joint work with Kostochka, Reiniger, West and Zhu.