A Note on the Thickness of Kimn

Abstract

The thickness \(\theta(G)\) of a graph \(G\) is the minimum number of planar spanning subgraphs into which \(G\) can be decomposed. In this note, we determine the thickness of the complete tripartite graph \(K_{l,m,n}\) (\(1 \leq m \leq n\)) for the following cases: (1) \(l + m \leq 5\); (2) \(l + m\) is even and \(n > \frac{1}{2}(l + m – 2)\); (3) \(l + m\) is odd and \(n > (l + m – 2)(l + m – 1)\).