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In this paper two generic properties are presented for graph maps. Letbe the space of continuous maps from the topological graph  X  into itself, equipped with the topology of uniform convergence. Then there is a residual subsetsuch that for every, all the scrambled sets of  f , as well as the set of chain recurrence points of  f , are nowhere dense and of zero Hausdorff dimension.

Scrambled sets and chain recurrence points of generic graph maps