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Brief Announcement: Exploring Word-Representable Temporal Graphs

Author Duncan Adamson

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  • Mathematics of computing → Graph algorithms
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  • Temporal Graphs
  • Word-Representable Graphs

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Abstract

Word-representable graphs are a subset of graphs that may be represented by a word w over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices alternate in the word w. We generalise this notion to temporal graphs, constructing timesteps by partitioning the word into factors (contiguous subwords) such that no factor contains more than one copy of any given symbol. With this definition, we study the problem of exploration, asking for the fastest schedule such that a given agent may explore all n vertices of the graph. We show that if the corresponding temporal graph is connected in every timestep, we may explore the graph in 2δ n timesteps, where δ is the lowest degree of any vertex in the graph. In general, we show that, for any temporal graph represented by a word of length at least n(2dn + d), with a connected underlying graph, the full graph can be explored in 2 d n timesteps, where d is the diameter of the graph.

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Duncan Adamson. Brief Announcement: Exploring Word-Representable Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 22:1-22:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.22

Author Details

Duncan Adamson
  • School of Computer Science, University of St Andrews, UK

References

  1. Duncan Adamson. Exploring word-representable temporal graphs, 2025. URL: https://doi.org/10.48550/arXiv.2502.07496.
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