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**1 - 3**of**3**### CONJECTURES ON COPS AND ROBBERS

"... Abstract. We consider some of the most important conjectures in the study of the game of Cops and Robbers and the cop num-ber of a graph. The conjectures touch on diverse areas such as algorithmic, topological, and structural graph theory. 1. ..."

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Abstract. We consider some of the most important conjectures in the study of the game of Cops and Robbers and the cop num-ber of a graph. The conjectures touch on diverse areas such as algorithmic, topological, and structural graph theory. 1.

### GRAPH SEARCHING AND RELATED PROBLEMS

"... Suppose that there is a robber hiding on vertices or along edges of a graph or digraph. Graph searching is concerned with finding the minimum number of searchers required to capture the robber. We survey the major results of graph searching problems, focusing on algorithmic, structural, and probabi ..."

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Suppose that there is a robber hiding on vertices or along edges of a graph or digraph. Graph searching is concerned with finding the minimum number of searchers required to capture the robber. We survey the major results of graph searching problems, focusing on algorithmic, structural, and probabilistic aspects of the field.