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math.CO2024
The Closed Geodetic Game: algorithms and strategies
Antoine Dailly, Harmender Gahlawat, Zin Mar Myint
The geodetic closure of a set S of vertices of a graph is the set of all vertices in shortest paths between pairs of vertices of S. A set S of vertices in a graph is geodetic if it…
cs.DM2024
On the Cop Number of String Graphs
Sandip Das, Harmender Gahlawat
Cops and Robber is a well-studied two-player pursuit-evasion game played on a graph, where a group of cops tries to capture the robber. The \emph{cop number} of a graph is the mini…