DROPS

Document

DOI: 10.4230/LIPIcs.FSTTCS.2025.10

Cat Herding Game Played on Infinite Trees

Authors: Rylo Ashmore and Sophie Pinchinat

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract

The game of Cat Herding is played on a graph between two players, the cat and the herder. The game setup consists of the cat choosing a starting vertex for their cat token. Then, both players alternate turns, beginning with the herder: they delete (any) one edge, called a cut, and the cat moves along a path to a new vertex. While this game has been studied on finite graph arenas regarding how optimally herder wins, we shift our attention to an infinite version of the game where the cat may now survive indefinitely. We show that cat winning positions in an infinite tree can be characterized by a second-order monadic statement, also amounting to having a complete infinite binary tree minor, or having uncountably many distinct rays. We take advantage of the logical characterization of cat winning positions to generalize a measure known as the cat number, to ordinals.

Cite as

Rylo Ashmore and Sophie Pinchinat. Cat Herding Game Played on Infinite Trees. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ashmore_et_al:LIPIcs.FSTTCS.2025.10,
  author =	{Ashmore, Rylo and Pinchinat, Sophie},
  title =	{{Cat Herding Game Played on Infinite Trees}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.10},
  URN =		{urn:nbn:de:0030-drops-250902},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.10},
  annote =	{Keywords: Pursuit-evasion games, Cat Herding, Cat number, Infinite trees, Monadic Second Order Logic, Ordinals}
}

Search Results

Documents authored by Ashmore, Rylo

Cat Herding Game Played on Infinite Trees

Abstract

Cite as

Thanks for your feedback!

Could not send message