Tutte Distinguished Lecture - Bojan Mohar

Title: Toward a Theory of Crossing-Critical Graphs

Abstract: 

The crossing number of a graph is defined as the minimum number of crossings of edges in a drawing of the graph in the plane. In his seminal 1970 paper Toward a Theory of Crossing Numbers, Tutte made a fundamental contribution by proving what is known today as the Hanani-Tutte Theorem. Since then, the theory of crossing numbers of graphs made a long way. The talk will outline a recent completion of a long-term project to give a structural description of crossing-critical graphs. These are graphs in which the removal of any edge decreases the crossing number.

This is joint work with Zdenek Dvorak and Petr Hlineny.