# On rectangle intersection graphs with stab number at most two

## Article Type

Research Article

## Publication Title

Discrete Applied Mathematics

## Abstract

Rectangle intersection graphs are the intersection graphs of axis-parallel rectangles in the plane. A graph G is said to be a k-stabbable rectangle intersection graph, or k-SRIG for short, if it has a rectangle intersection representation in which k horizontal lines can be placed such that each rectangle intersects at least one of them. In this article, we introduce some natural subclasses of 2-SRIG and study the containment relationships among them. It is shown that one of these subclasses can be recognized in linear-time if the input graphs are restricted to be triangle-free. We also make observations about the chromatic number of 2-SRIGs. It is shown that the CHROMATIC NUMBER problem is NP-complete for 2-SRIGs, by showing that the problem is NP-complete for 2-row B0-VPGs. This is a strengthening of some known results from the literature.

## First Page

354

## Last Page

365

## DOI

10.1016/j.dam.2020.11.003

## Publication Date

1-31-2021

## Recommended Citation

Chakraborty, Dibyayan; Das, Sandip; Francis, Mathew C.; and Sen, Sagnik, "On rectangle intersection graphs with stab number at most two" (2021). *Journal Articles*. 2118.

https://digitalcommons.isical.ac.in/journal-articles/2118