Discussion
The thickness of a graph G is defined as minimum number of (edge-disjoint) planar subgraphs into which G can be decomposed. The thickness of G is defined as θ(G). What is the thickness of planar graph ?
Answer: A
The thickness of a planar graph is 1.
Thickness θ(G) is the minimum number of planar subgraphs whose union is G. A planar graph can be drawn in the plane without crossings, so it is already one planar subgraph and needs no decomposition: θ(G) = 1.
Thickness 2 or more is needed only for non-planar graphs. For example, \(K_{5}\) and \(K_{3,3}\) have thickness 2, because each can be split into two planar parts but not drawn as one. Values 3 and 4 belong to still larger complete graphs.
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