The thickness of fan-planar graphs is at most three

TL;DR

This paper proves that strongly fan-planar graphs have a thickness of at most three, with bipartite graphs requiring only two colors for non-crossing edge coloring, advancing understanding of their structural properties.

Contribution

The paper establishes an upper bound of three on the thickness of strongly fan-planar graphs and shows bipartite cases need only two colors, providing new bounds on their edge coloring.

Findings

Thickness of strongly fan-planar graphs is at most three.

Bipartite strongly fan-planar graphs have thickness at most two.

Edges in these graphs can be colored with minimal colors to avoid crossings.

Abstract

We prove that in any strongly fan-planar drawing of a graph G the edges can be colored with at most three colors, such that no two edges of the same color cross. This implies that the thickness of strongly fan-planar graphs is at most three. If G is bipartite, then two colors suffice to color the edges in this way.