In graph theory, a haven is a certain type of function on sets of vertices in an undirected graph. If a haven exists, it can be used by an evader to win a pursuit–evasion game on the graph, by consulting the function at each step of the game to determine a safe set of vertices to move into. Havens were first introduced by Seymour & Thomas (1993) as a tool for characterizing the treewidth of graphs.[1] Their other applications include proving the existence of small separators on minor-closed families of graphs,[2] and characterizing the ends and clique minors of infinite graphs.[3][4]
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