Outerthickness θ_o(G): decompose edges into minimum number of outerplanar subgraphs. More restrictive than thickness (which uses planar subgraphs). θ_o ≥ θ always. Outerplanar graphs have all vertices on outer face.
How to Use
Select graph:
- θ_o: Outerthickness
- vs θ: Compare
- OP: Outerplanar?
Outerplanar Subgraphs
Outerplanar: planar + all vertices on outer face. At most 2n-3 edges. More restrictive than planar (at most 3n-6). So outerthickness ≥ thickness. Gap can be significant for dense graphs.
Bounds
θ_o ≥ ⌈m/(2n-3)⌉. Planar: θ_o ≤ 2. K_n: θ_o = ⌈(n+1)/4⌉ approximately. Related to book thickness by θ_o ≤ bt(G). Nice connections to linear layouts.
Step-by-Step Instructions
- 1Select graph.
- 2Compute θ_o.
- 3Compare with θ.
- 4Check outerplanarity.
- 5Apply bounds.