Albertson conjecture and related problems

October 14 to October 18, 2024

at the

American Institute of Mathematics, Pasadena, California

organized by

Janos Pach, Andrew Suk, and Geza Toth

Original Announcement

This workshop will be devoted to the Albertson conjecture and on other problems related to crossing numbers. The crossing number of a graph is the minimum number of edge crossings in a drawing of the graph in the plane. Determining or estimating the crossing number of a graph is one of the oldest problems in graph theory, with over 700 papers written on the subject. In 2007, Albertson made a tantalizing conjecture which would establish a relationship between the crossing number and the chromatic number of a graph. His conjecture states that if a graph requires at least $r$ colors to properly color its vertices, then the crossing number of the graph is at least the crossing number of the complete graph on $r$ vertices. We believe that the time is ripe to revisit this conjecture. We also intend to study some related problems which have proved particularly fruitful in recent years.

The main topics for the workshop are:

  1. Albertson’s conjecture
  2. Quasi planar graphs
  3. Coloring intersection graphs.

Material from the workshop

A list of participants.

The workshop schedule.