Why it matters

Real graphs often near-planar. Understanding enables efficient algorithms.

Advertisement

The architecture

Planar: V - E + F = 2 (Euler's formula).

Sparse: |E| ≤ 3|V| - 6.

Planar graph propertiesEuler's formulaV-E+F=2Sparsity|E|≤3|V|-6Planar separatorsO(√n)Planar separator theorem enables many divide-conquer algorithms
Planar properties.
Advertisement

How it works end to end

Planar separator: any planar graph has separator of size O(√n).

Shortest path in planar: O(n log n) instead of O(n log n + m).

Max flow in planar: O(n^1.5).

Applications: road networks, VLSI, GIS.