Cutwidth Bounds via Vertex Partitions
Abstract
We study the cutwidth measure on graphs and ways to bound the cutwidth of a graph by partitioning its vertices. We consider bounds expressed as a function of two quantities: on the one hand, the maximal cutwidth y of the subgraphs induced by the classes of the partition, and on the other hand, the cutwidth x of the quotient multigraph obtained by merging each class to a single vertex. We consider in particular the decomposition of directed graphs into strongly connected components (SCCs): in this case, y is the maximal cutwidth of an SCC, and x is the cutwidth of the directed acyclic condensation multigraph. We show that the cutwidth of a graph is always in O(x + y), specifically it can be upper bounded by 1.5x + y. We also show a lower bound justifying that the constant 1.5 cannot be improved in general
Cite
@article{arxiv.2504.01574,
title = {Cutwidth Bounds via Vertex Partitions},
author = {Antoine Amarilli and Benoît Groz},
journal= {arXiv preprint arXiv:2504.01574},
year = {2025}
}
Comments
14 pages including appendix. This version (relative to v1) fixes an important mix-up in the abstract, along with some minor changes