Segment representation of a subclass of co-planar graphs

Abstrakt

A graph is a segment graph if its vertices can be mapped to line segments in the plane such that two vertices are adjacent if and only if their corresponding line segments intersect. Kratochvil and Kubena asked the question of whether the complements of planar graphs, called co-planar graphs, are segment graphs.

We show here that the complements of all partial 2-trees are segment graphs.

Klíčová slova

• Geometric intersection graphs
• Segment graphs
• Co-planar graphs
• Partial 2-trees