Word-Representable Graphs and Locality of Words
Combinatorics
2025-06-25 v1 Formal Languages and Automata Theory
Abstract
In this work, we investigate the relationship between -repre\-sentable graphs and graphs representable by -local words. In particular, we show that every graph representable by a -local word is -representable. A previous result about graphs represented by -local words is revisited with new insights. Moreover, we investigate both classes of graphs w.r.t. hereditary and in particular the speed as a measure. We prove that the latter ones belong to the factorial layer and that the graphs in this classes have bounded clique-width.
Cite
@article{arxiv.2506.19493,
title = {Word-Representable Graphs and Locality of Words},
author = {Philipp Böll and Pamela Fleischmann and Annika Huch and Jana Kreiß and Tim Löck and Kajus Park and Max Wiedenhöft},
journal= {arXiv preprint arXiv:2506.19493},
year = {2025}
}