2026-07-23T04:52:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25033 2026-02-09T07:53:55Z ddc:004 open_access

Reconfigurations of Plane Caterpillars and Paths (Poster Abstract) Antić, Todor Gamboa Quintero, Guillermo Glišić, Jelena reconfiguration graph caterpillar path geometric graph 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Todor Antić and Guillermo Gamboa Quintero and Jelena Glišić 2025 Is Part Of LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.GD.2025.47 urn:nbn:de:0030-drops-250337 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.47 eng https://creativecommons.org/licenses/by/4.0/legalcode