# The 4-girth-thickness of the complete graph

## TL;DR

This paper introduces the concept of 4-girth-thickness for graphs, specifically calculating it for complete graphs, revealing a formula that applies to all but two specific cases.

## Contribution

It defines the 4-girth-thickness of graphs and determines its exact value for all complete graphs except for two special cases.

## Key findings

- The 4-girth-thickness of K_n is eil((n+2)/4)or n ,10.
- eil((n+2)/4)pplies to all complete graphs except K_6 and K_{10}.
- The 4-girth-thickness of K_6 is 3.

## Abstract

In this paper, we define the $4$-girth-thickness $\theta(4,G)$ of a graph $G$ as the minimum number of planar subgraphs of girth at least $4$ whose union is $G$. We obtain the $4$-girth-thickness of the arbitrary complete graph $K_n$ getting that $\theta(4,K_n)=\left\lceil \frac{n+2}{4}\right\rceil$ for $n\not=6,10$ and $\theta(4,K_6)=3$.