# Stability of Critical p-Improper Interval Graphs

## TL;DR

This paper investigates the stability of critical p-improper interval graphs by analyzing how their impropriety spectrum changes upon removal of a vertex, contributing to understanding their structural robustness.

## Contribution

It introduces the concept of stability in critical p-improper interval graphs and explores their impropriety spectrum after vertex removal.

## Key findings

- Characterization of the impropriety spectrum upon vertex removal
- Insights into the structural robustness of critical p-improper interval graphs
- Extension of the theory of interval graph impropriety

## Abstract

A $p$-improper interval graph is an interval graph that has an interval representation in which no interval contains more than $p$ other intervals. A critical $p$-improper interval graph is $p-1$ improper when any vertex is removed. In this paper we investigate the spectrum of impropriety of critical $p$-improper interval graphs upon the removal of a single vertex, which is informally known as the stability of the graph.