arXiv subjects

Robert Ferguson

Publications and source records attributed to Robert Ferguson.

3 recordsLinked to original sources

arXiv2021

Letter graphs and geometric grid classes of permutations

We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of their respective classes of objects. We prove that these notions are equivalent in the sense that a permutation class is geometrically griddable if and only if the corresponding class of inversion graphs has bounded lettericity.

math.CO↗

arXiv2021

Letter graphs and modular decomposition

We prove that if the prime graphs in a graph class have bounded lettericity, then the entire class has bounded lettericity if and only if it does not contain arbitrary large matchings, co-matchings, or a family of graphs that we call stacked paths.

math.CO↗

arXiv2020

On the Lettericity of Paths

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

math.CO↗