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The $g$-girth-thickness $\theta(g,G)$ of a graph $G$ is the minimum number ofplanar subgraphs of girth at least $g$ whose union is $G$. In this note, wegive the $4$-girth-thickness $\theta(4,L(K_n))$ of the line graph of thecomplete graph $L(K_n)$ when $n$ is even. We also give the minimum number ofsubgraphs of $L(K_n)$, which are of girth at least $4$ and embeddable on theprojective plane, whose union is $L(K_n)$.

On the 4-girth-thickness of the line graph of the complete graph