TL;DR
This paper determines the minimum number of planar subgraphs needed to cover specific complete multipartite graphs, advancing understanding of their structural properties.
Contribution
It provides the exact thickness values for K_1,n,n, K_2,n,n, and K_1,1,n,n, which were previously unknown.
Findings
Thickness of K_1,n,n and K_2,n,n determined.
Thickness of K_1,1,n,n established.
Results contribute to graph decomposition theory.
Abstract
The thickness of a graph G is the minimum number of planar subgraphs whose union is G. In this paper, we obtain the thickness of complete 3-partite graph K_1,n,n, K_2,n,n and complete 4-partite graph K_1,1,n,n.
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