Abstract
In a recent paper, Baradol, Gopal and Radenović (2020) study the contraction properties of mappings on rectangular metric spaces endowed with a digraph. In this paper, we show that a class of mappings on dismantlable undirected graphs have a natural contraction-like property acting on a spanning tree of the graph. We propose further characterizations of dismantlable graphs and apply our results to pursuit-evasion games on graphs.
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