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In this work, we investigate the relationship between k-representable 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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Word-Representable Graphs and Locality of Words

  • 会议论文

  • 发表日期：

    2025年

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  • Philipp Böll,
  • Pamela Fleischmann,
  • Annika Huch,
  • Jana Kreiß,
  • Tim Löck,
  • Kajus Park,
  • Max Wiedenhöft

摘要

In this work, we investigate the relationship between k-representable 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.