The goal of the project Beyond the Four Color Theorem is to develop generalizations of the Four Color Theorem in setting such as graphs drawn in the plane with only one crossing, or planar after removal of one edge, or (optimistically) drawn on the torus. We expect to combine the methods from the proof of the Four Color Theorem (reducible configurations, discharging) with topological tools to describe the structure of the obstructions to 4-colorability.

The project is funded in years 2024–2028 by the ERC-CZ grant LL2328 of the Ministry of Education of Czech Republic.

Project team:

• Zdeněk Dvořák (principal investigator)
• Robert Šámal (senior researcher)
• Martin Tancer (senior researcher)
• David Mikšaník (doctoral student)
• An open postdoctoral position: We especially look for candidates with background in graph coloring or computational topology.