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

Authors

  • Xia Guo Tianjin University, China
  • Yan Yang Tianjin University, China

DOI:

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

Keywords:

Thickness, 4-girth-thickness, complete tripartite graph

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).

Published

2018-08-23

Issue

Section

Articles