Intersection Graphs of Rays and Grounded Segments

Understand

We consider several classes of intersection graphs of line segments in the plane and prove new equality and separation results between those classes.

• In particular, we show that: (1) intersection graphs of grounded segments and intersection graphs of downward rays form the same graph class, (2) not every intersection graph of rays is an intersection graph of downward rays, and (3) not every intersection graph of rays is an outer segment graph.
• The first result answers an open problem posed by Cabello and Jej\v{c}i\v{c}.
• The third result confirms a conjecture by Cabello.