Geodesic
A note on the 4-girth-thickness of K_n,n,n
Ars Mathematica Contemporanea, Tome 16 (2019) no. 1, pp. 19-24.

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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 Kn, n, n is ⌈(n + 1) / 2⌉ except for θ(4, K1, 1, 1) = 2. And we also show that the 4-girth-thickness of the complete graph K10 is three which disprove the conjecture posed by Rubio-Montiel concerning to θ(4, K10).
DOI : 10.26493/1855-3974.1488.182
Keywords: Thickness, 4-girth-thickness, complete tripartite graph 
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Xia Guo; Yan Yang. A note on the 4-girth-thickness of K_n,n,n. Ars Mathematica Contemporanea, Tome 16 (2019) no. 1, pp. 19-24. doi : 10.26493/1855-3974.1488.182. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1488.182/

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