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math.CO2026
Patrolling cop vs omniscient robber
Nina Chiarelli, Paul Dorbec, MiloÅ¡ StojakoviÄ +1
We study a variant of the classical Cops and Robbers game with one cop and one robber. The cop follows a fixed walk on the graph, called a patrol, that is chosen before the game be…
math.CO2025
Cayley trees and increasing 1,2-trees: let's twist!
Julien Courtiel, Matthieu Dien, Paul Dorbec
An increasing 1,2-tree is a labeled graph formed by starting with a vertex and then repeatedly attaching a leaf to a vertex or a triangle to an edge, the labeling of the vertices c…
math.CO2024
An exploration of the balance game
Paul Dorbec, Michael A. Henning, Zsolt Tuza +1
The balance game is played on a graph by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of . Admirable labels the selected vertices b…