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arXiv · 2506.19493

Word-Representable Graphs and Locality of Words

Philipp Böll·Pamela Fleischmann·Annika Huch·Jana Kreiß·Tim Löck·Kajus Park·Max Wiedenhöft
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Abstract

In this work, we investigate the relationship between $k$-repre\-sentable graphs and graphs representable by $k$-local words. In particular, we show that every graph representable by a $k$-local word is $(k+1)$-representable. A previous result about graphs represented by $1$-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.

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Philipp Böll, Pamela Fleischmann, Annika Huch, Jana Kreiß, Tim Löck, Kajus Park, Max Wiedenhöft. 2025-06-24. Word-Representable Graphs and Locality of Words. https://arxiv.org/abs/2506.19493

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