Geodesic
The 4-girth-thickness of the complete graph
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 319-327.

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In this paper, we define the 4-girth-thickness θ(4, G) of a graph G as the minimum number of planar subgraphs of girth at least 4 whose union is G. We prove that the 4-girth-thickness of an arbitrary complete graph Kn, θ(4, Kn), is ⌈(n+2)/4⌉ for n ≠ 6, 10 and θ(4, K6)=3.
DOI : 10.26493/1855-3974.1349.b67
Keywords: Thickness, planar decomposition, girth, complete graph 
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Christian Rubio-Montiel. The 4-girth-thickness of the complete graph. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 319-327. doi : 10.26493/1855-3974.1349.b67. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1349.b67/

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