A note on the 4-girth-thickness of Ksub{n,n,n} - Guo, Xia (Ars mathematica contemporanea, 2019)
The 4-girth-thickness ?$θ(4, G)$? 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 ?$θ(4, K_{1, 1, 1}) = 2$?. And we also show that the 4-girth-thickness of the complete graph ?$K_{10}$? is three which disprove the conjecture posed by C. Rubio-Montiel Ars Math. Contemp. 14, No. 2, 319--327 (2018) concerning to ?$θ(4, K_{10})$?.
Keywords: 4-girth-thickness; 4-ožinska debelina; complete tripartite graph; debelina; polni tridelni graf; thickness