4-cop-win graphs have at least 19 vertices

DOI10.1016/j.dam.2021.05.012zbMath1464.91026arXiv2006.02998OpenAlexW3033968741MaRDI QIDQ2032980

Jérémie Turcotte, Samuel Yvon

Publication date: 14 June 2021

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.02998

zbMATH Keywords

extremal problemscomputer-assisted proofcops and robberscop numbergraph construction4-cop-win

Mathematics Subject Classification ID

Games involving graphs (91A43) Games on graphs (graph-theoretic aspects) (05C57)

Uses Software

• Mathematica
• nauty
• Traces
• Julia
• GitHub
• LightGraphs.jl
• Cop-Number

Cites Work

• Unnamed Item
• Characterizations of \(k\)-copwin graphs
• Cops and robbers from a distance
• A game of cops and robbers
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• Cops and robbers in graphs with large girth and Cayley graphs
• On a pursuit game played on graphs for which a minor is excluded
• On the cop number of a graph
• A note on \(k\)-cop-win graphs
• Vertex-to-vertex pursuit in a graph
• Meyniel's conjecture on the cop number: a survey
• On the cop number of toroidal graphs
• Topological directions in cops and robbers
• Practical graph isomorphism. II.
• Variations on cops and robbers
• On Meyniel's conjecture of the cop number
• Julia: A Fresh Approach to Numerical Computing
• On the Conjecture of the Smallest 3-Cop-Win Planar Graph
• A Bound for the Cops and Robbers Problem
• On the minimum order of k-cop-win graphs
• Conjectures on Cops and Robbers
• The smallest graph of girth 5 and valency 4

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