The 3-symmetric Pseudolinear Crossing Number of $K_{33}$

TL;DR

This paper proves that the 3-symmetric rectilinear and pseudolinear crossing numbers of the complete bipartite graph K_{33} are equal, both being 14,634, establishing a precise crossing number value for this graph.

Contribution

The paper establishes the equality of 3-symmetric rectilinear and pseudolinear crossing numbers for K_{33}, providing an exact crossing number value.

Findings

Both crossing numbers are equal to 14,634.

The equality of these crossing numbers is rigorously proven.

The result advances understanding of symmetric crossing numbers in graph theory.

Abstract

We show that the 3-symmetric rectilinear and the 3-symmetric pseudolinear crossing numbers of $K_{33}$ are equal. Specifically, we prove that $\operatorname{sym}-\overline{\operatorname{cr}}_3(K_{33}) = 14 634 = \operatorname{sym}-\widetilde{\operatorname{cr}}_3(K_{33})$.