Chordal graphs are easily testable

TL;DR

This paper proves that chordal graphs can be efficiently tested by examining small random vertex subsets, providing a probabilistic method to determine chordality with high confidence.

Contribution

It establishes the first known property testing algorithm for chordal graphs, showing they are easily testable with a constant number of random vertices.

Findings

Chordal graphs are easily testable with a constant number of samples.

Random vertex subsets can reliably detect non-chordality.

The result answers an open question in graph property testing.

Abstract

We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant $c>0$ such that, if adding/removing at most $\epsilon n^2$ edges to a graph $G$ with $n$ vertices does not make it chordal, then a set of $(1/\epsilon)^c$ vertices of $G$ chosen uniformly at random induces a graph that is not chordal with probability at least $1/2$. This answers a question of Gishboliner and Shapira.