On the complexity of embedding in graph products
Computational Geometry
2026-01-21 v1 Computational Complexity
Abstract
Graph embedding, especially as a subgraph of a grid, is an old topic in VLSI design and graph drawing. In this paper, we investigate related questions concerning the complexity of embedding a graph in a host graph that is the strong product of a path with a graph that satisfies some properties, such as having small treewidth, pathwidth or tree depth. We show that this is NP-hard, even under numerous restrictions on both and . In particular, computing the row pathwidth and the row treedepth is NP-hard even for a tree of small pathwidth, while computing the row treewidth is NP-hard even for series-parallel graphs.
Cite
@article{arxiv.2303.17028,
title = {On the complexity of embedding in graph products},
author = {Therese Biedl and David Eppstein and Torsten Ueckerdt},
journal= {arXiv preprint arXiv:2303.17028},
year = {2026}
}