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math.CO2025
The radius capture number
Tanja Dravec, Vesna Iršič Chenoweth, Andrej Taranenko
In the classic cop and robber game, two players--the cop and the robber--take turns moving to a neighboring vertex or staying at their current position. The cop aims to capture the…
math.CO2024
The strong vertex span of trees
Mateja Grašič, Chris Mouron, Andrej Taranenko
The strong vertex (edge) span of a given graph is the maximum distance that two players can maintain at all times while visiting all vertices (edges) of and moving either t…
math.CO2024
Graphs with span 1 and shortest optimal walks
Tanja Dravec, Mirjana Mikalački, Andrej Taranenko
A span of a given graph is the maximum distance that two players can keep at all times while visiting all vertices (edges) of and moving according to certain rules, that pr…