The 4-girth-thickness of the complete graph

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 $\theta (4,K_n)=\lceil \frac{n+2}{4}\rceil$ for $n\ne 6,10$ and $\theta (4,K_6)=3$.

9 pages, 8 figures

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