On the complexity of embedding in graph products
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908771179036672 |
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| author | Biedl, Therese Eppstein, David Ueckerdt, Torsten |
| author_facet | Biedl, Therese Eppstein, David Ueckerdt, Torsten |
| contents | 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 $G$ in a host graph that is the strong product of a path $P$ with a graph $H$ 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 $G$ and $H$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17028 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the complexity of embedding in graph products Biedl, Therese Eppstein, David Ueckerdt, Torsten Computational Geometry Computational Complexity 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 $G$ in a host graph that is the strong product of a path $P$ with a graph $H$ 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 $G$ and $H$. 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. |
| title | On the complexity of embedding in graph products |
| topic | Computational Geometry Computational Complexity |
| url | https://arxiv.org/abs/2303.17028 |