Contact graphs of boxes with unidirectional contacts

TL;DR

This paper investigates a special class of intersection graphs formed by boxes with unidirectional contacts, revealing structural properties and raising questions about their characteristics.

Contribution

It provides new structural insights into contact graphs of boxes with unidirectional contacts and explores their chromatic properties.

Findings

Graphs can have arbitrarily large chromatic number

They are triangle-free

Structural properties are identified

Abstract

This paper is devoted to the study of particular geometrically defined intersection classes of graphs. Those were previously studied by Magnant and Martin, who proved that these graphs have arbitrary large chromatic number, while being triangle-free. We give several structural properties of these graphs, and we raise several questions.