# The thickness of the Kronecker product of graphs

## TL;DR

This paper establishes bounds and exact values for the thickness of the Kronecker product of graphs, advancing understanding of graph planarity properties in complex graph constructions.

## Contribution

It provides sharp bounds and exact thickness numbers for specific Kronecker product graphs, a novel contribution to graph theory.

## Key findings

- Sharp bounds for the thickness of G×H
- Exact thickness for K_n×K_2, K_{m,n}×K_2, and K_{n,n,n}×K_2
- Enhanced understanding of planarity in Kronecker product graphs

## Abstract

The thickness of a graph $G$ is the minimum number of planar subgraphs whose union is $G$. In this paper, we present sharp lower and upper bounds for the thickness of the Kronecker product $G\times H$ of two graphs $G$ and $H$. We also give the exact thickness numbers for the Kronecker product graphs $K_n\times K_2$, $K_{m,n}\times K_2$ and $K_{n,n,n}\times K_2$.