A lower bound on the tree-width of graphs with irrelevant vertices
Discrete Mathematics
2019-01-15 v1 Combinatorics
Abstract
For their famous algorithm for the disjoint paths problem, Robertson and Seymour proved that there is a function such that if the tree-width of a graph with pairs of terminals is at least , then contains a solution-irrelevant vertex (Graph Minors. XXII., JCTB 2012). We give a single-exponential lower bound on . This bound even holds for planar graphs.
Cite
@article{arxiv.1901.04325,
title = {A lower bound on the tree-width of graphs with irrelevant vertices},
author = {Isolde Adler and Philipp Klaus Krause},
journal= {arXiv preprint arXiv:1901.04325},
year = {2019}
}