A note on the 4-girth-thickness of Kn,n,n

Xia Guo, Yan Yang

Abstract


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).


Keywords


Thickness, 4-girth-thickness, complete tripartite graph

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DOI: https://doi.org/10.26493/1855-3974.1488.182

ISSN: 1855-3974

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