We prove that if every subgraph of a graph G has a balanced separation of order at most a then G has treewidth at most 15a. This establishes a linear dependence between the treewidth and the separation number.
@article{arxiv.1408.3869,
title = {Treewidth of graphs with balanced separations},
author = {Zdenek Dvorak and Sergey Norin},
journal= {arXiv preprint arXiv:1408.3869},
year = {2018}
}
Comments
Final version accepted for publication in J. Comb. Theory B