Note on the thickness of the Cartesian product of a complete graph and a path

TL;DR

This paper calculates the thickness of specific Cartesian products of complete graphs and paths, expanding understanding of graph embedding properties.

Contribution

It determines the thickness of K_{6p+4} × P_2 and K_8 × P_m for various parameters, providing new exact values.

Findings

Thickness of K_{6p+4} × P_2 for p ≥ 0 is established.

Thickness of K_8 × P_m for m ≥ 1 is determined.

Results contribute to graph embedding and topological graph theory.

Abstract

We determine the thickness of the Cartesian product $K_{6p+4} \square P_2$ for $p \ge 0$ and of the Cartesian product $K_8 \square P_m$ for $m \ge 1$, where $K_n$ and $P_m$ denote the complete graph on $n$ vertices and the path on $m$ vertices, respectively.