English

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 kk-repre\-sentable graphs and graphs representable by kk-local words. In particular, we show that every graph representable by a kk-local word is (k+1)(k+1)-representable. A previous result about graphs represented by 11-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.

Keywords

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}
}