A note on the 4-girth-thickness of K_{n,n,n}

Abstract

The $4$-girth-thickness $\theta (4,G)$ of a graph $G$ is the minimum number of planar subgraphs of girth at least four whose union is $G$. In this paper, we obtain that the 4-girth-thickness of complete tripartite graph $K_{n,n,n}$ is $\lceil \frac{n+1}{2}\rceil$ except for $\theta (4,K_{1,1,1})=2$. And we also show that the $4$-girth-thickness of the complete graph $K_{10}$ is three which disprove the conjecture $\theta (4,K_{10})=4$ posed by Rubio-Montiel (Ars Math Contemp 14(2) (2018) 319).

References in corpus (1)

• The 4-girth-thickness of the complete graph