Abstract
In the one-visibility cops and robber game on a graph, the robber is visible to the cops only when the robber is in the closed neighbourhood of the vertices occupied by the cops. The one-visibility copnumber of a graph is the minimum number of cops required to capture the robber on the graph. In this paper, we investigate the one-visibility cops and robber game on trees. For trees, we introduce a key structure, called road, for characterising optimal cop-win strategies. We give an O(nlogn) time algorithm to compute an optimal cop-win strategy for a tree with n vertices. We also establish relations between zero-visibility and one-visibility copnumbers on trees.
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