Characterization of Level Non-planar Graphs by Minimal Patterns

  title={Characterization of Level Non-planar Graphs by Minimal Patterns},
  author={Patrick Healy and Ago Kuusik and Sebastian Leipert},
In this paper we develop a characterisation of minimal non-planarity of level graphs. We show that a level minimal non-planar (LMNP) graph is completely characterised by either a tree, a level non-planar cycle or a level planar cycle with certain path augmentations. We discuss the usefulness of these characterisations in the context of an branch-and-cut Integer Linear Programming implementation of the Maximum Level Planar Subgraph (MLPS) problem and conjecture that the inequalities associated… CONTINUE READING