MathDBInfinite-family conjecture for 4-edge-critical pseudocircle arrangement graphs
Infinite-family conjecture for 4-edge-critical pseudocircle arrangement graphs
A simple arrangement is an arrangement of pseudocircles with no three curves meeting at one point, and an arrangement graph is 4-edge-critical when it is 4-chromatic and deleting any edge decreases its chromatic number.
Infinite-family conjecture. There exists an infinite family of simple arrangement graphs of 4-edge-critical arrangements of pseudocircles.
The paper constructs several examples and discusses infinite families of related critical planar graphs, but the asserted infinite family of simple pseudocircle arrangement graphs remains open.
Sources & referencesView supporting material
Primary source
Man-Kwun Chiu, Stefan Felsner, Manfred Scheucher, Felix Schröder, Raphael Steiner and Birgit Vogtenhuber, “Coloring circle arrangements: New 4-chromatic planar graphs”, arXiv:2205.08181 (2022).
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