On a tree-based variant of bandwidth and forbidding simple topological minors
Discrete Mathematics
2025-02-18 v1 Computational Complexity
Data Structures and Algorithms
Combinatorics
Abstract
We obtain structure theorems for graphs excluding a fan (a path with a universal vertex) or a dipole () as a topological minor. The corresponding decompositions can be computed in FPT linear time. This is motivated by the study of a graph parameter we call treebandwidth which extends the graph parameter bandwidth by replacing the linear layout by a rooted tree such that neighbours in the graph are in ancestor-descendant relation in the tree. We deduce an approximation algorithm for treebandwidth running in FPT linear time from our structure theorems. We complement this result with a precise characterisation of the parameterised complexity of computing the parameter exactly.
Cite
@article{arxiv.2502.11674,
title = {On a tree-based variant of bandwidth and forbidding simple topological minors},
author = {Hugo Jacob and William Lochet and Christophe Paul},
journal= {arXiv preprint arXiv:2502.11674},
year = {2025}
}