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Closure Under Minors of Undirected Entanglement

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Abstract:

Entanglement is a digraph complexity measure that origins in fixed-point theory. Its purpose is to count the nested depth of cycles in digraphs. In this paper we prove that the class of undirected graphs of entanglement at most $k$, for arbitrary fixed $k \in \mathbb{N}$, is closed under taking minors. Our proof relies on the game theoretic characterization of entanglement in terms of Robber and Cops games.

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