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Reconfigurations of Plane Caterpillars and Paths (Poster Abstract)

Authors Todor Antić , Guillermo Gamboa Quintero , Jelena Glišić

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Combinatorics
Keywords
  • reconfiguration graph
  • caterpillar
  • path
  • geometric graph

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Abstract

Let S be a point set in the plane, and let 𝒫(S) and 𝒞(S) be the sets of all plane spanning paths and caterpillars on S. We study reconfiguration operations on 𝒫(S) and 𝒞(S). In particular, we prove that all of the commonly studied reconfigurations on plane spanning trees still yield connected reconfiguration graphs for caterpillars when S is in convex position. If S is in general position, we show that the rotation, compatible flip and flip graphs of 𝒞(S) are connected while the slide graph is sometimes disconnected, but always has a component of size 1/4(3ⁿ-1). We then study sizes of connected components in reconfiguration graphs of plane spanning paths. In this direction, we show that no component of size at most 7 can exist in the flip graph on 𝒫(S).

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Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić. Reconfigurations of Plane Caterpillars and Paths (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 47:1-47:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.47

Author Details

Todor Antić
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Guillermo Gamboa Quintero
  • Computer Science Institute of Charles University, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Jelena Glišić
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

Funding

  • Antić, Todor: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR) and by SVV–2023–260699.
  • Gamboa Quintero, Guillermo: supported by the GAČR grant 22-17398S and the Charles University project PRIMUS/24/SCI/012.
  • Glišić, Jelena: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR) and by SVV–2023–260699.

Acknowledgements

We would like to thank Jan Kynčl and Pavel Valtr for proposing the problems and for all of the helpful discussions during the combinatorial problems seminar at Charles University. We also thank Daniel Perz for pointing out the existence of an isolated vertex in G_𝒞^{slide}(S), for his help in finding literature for this paper, and helpful comments.

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References

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    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.24692
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