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 \(\theta(G)\). What is the thickness of planar graph ?
1
1 option is correct.
The thickness \(\theta(G)\) of a graph is defined as \(\theta(G) = \min \{k : G = G_{1} \cup G_{2} \cup \cdots \cup G_{k},\ G_{i}\ \text{planar}\}\) — the smallest number of edge-disjoint planar subgraphs that cover every edge of \(G\).
If \(G\) is already planar, the trivial cover \(G = G_{1}\) with a single planar subgraph works, so \(\theta(G) = 1\). Higher thickness applies to non-planar graphs like \(K_{5}\) or \(K_{3,3}\) that fail Kuratowski's criterion.
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