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A lower bound on the tree-width of graphs with irrelevant vertices

Published 14 Jan 2019 in cs.DM and math.CO | (1901.04325v1)

Abstract: For their famous algorithm for the disjoint paths problem, Robertson and Seymour proved that there is a function $f$ such that if the tree-width of a graph $G$ with $k$ pairs of terminals is at least $f(k)$, then $G$ contains a solution-irrelevant vertex (Graph Minors. XXII., JCTB 2012). We give a single-exponential lower bound on $f$. This bound even holds for planar graphs.

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