# On Chordal Graph and Line Graph Squares

## TL;DR

This paper studies the conditions under which the squares and line graph squares of graphs are chordal, providing new characterizations and forbidden subgraph conditions for these properties.

## Contribution

It offers a new sufficient condition for the chordality of graph squares and characterizes chordality via forbidden subgraphs, extending to line graph squares.

## Key findings

- Proves a sufficient condition for chordality of graph squares without long induced cycles.
- Characterizes chordality of graph squares using forbidden subgraphs.
- Provides a characterization of chordality for line graph squares.

## Abstract

In this work we investigate the chordality of squares and line graph squares of graphs. We prove a sufficient condition for the chordality of squares of graphs not containing induced cycles of length at least five. Moreover, we characterize the chordality of graph squares by forbidden subgraphs. Transferring that result to line graphs allows us to characterize the chordality of line graph squares.