摘要 : 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 mini... 展开 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 (n logn) 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.(c) 2022 Elsevier B.V. All rights reserved. 收起