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math.CO2026
Results on Cartesian -capacity of graphs
Mateja GraÅ¡iÄ, Christopher Mouron, AljoÅ¡a Å ubaÅ¡iÄ +2
The concept of graph capacity extends graph span by considering the maximum number of agents that can simultaneously traverse a graph while preserving a prescribed minimum distance…
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…