# The smallest art gallery not guarded by every third vertex

## TL;DR

This paper explores the limitations of a guard placement strategy in polygonal art galleries, providing a minimal counterexample that demonstrates the strategy's failure for certain nine-sided galleries.

## Contribution

It introduces a minimal nine-sided gallery where placing guards at every third corner does not suffice, challenging existing guard placement assumptions.

## Key findings

- Counterexample gallery with 9 sides where strategy fails
- Proof of minimality of the example
- Insights into guard placement limitations

## Abstract

A polygonal art gallery can be observed by guards placed at one third of its corners. However, the strategy of placing guards at every third corner does not work for all art galleries. In this note, we provide an example of a nine-sided art gallery for which this strategy fails, and prove that this example is minimal.