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02/28/2023
Improved bounds on the cop number when forbidding a minor
Andreae (1986) proved that the cop number of connected H-minor-free grap...
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01/30/2023
Cops and robbers on P_5-free graphs
We prove that every connected P_5-free graph has cop number at most two,...
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07/08/2022
The Burning Number Conjecture Holds Asymptotically
The burning number b(G) of a graph G is the smallest number of turns req...
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06/04/2020
4-cop-win graphs have at least 19 vertices
We show that the cop number of any graph on 18 or fewer vertices is at m...
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01/09/2020