On the Lettericity of Paths

TL;DR

This paper proves a precise formula for the lettericity of paths with n vertices, confirming a conjecture and advancing understanding of graph lettericity.

Contribution

It establishes the exact lettericity of paths, confirming Petkov{ }ec's conjecture and providing a definitive result in the study of graph lettericity.

Findings

Lettericity of an n-vertex path is exactly ⌊(n+4)/3⌋.

Confirmed Petkov{ }ec's conjecture on path lettericity.

Provides a closed-form formula for path lettericity.

Abstract

Verifying a conjecture of Petkov{\v{s}}ec, we prove that the lettericity of an n-vertex path is precisely $\left\lfloor \frac{n+4}{3}\right\rfloor$.