Planarizing Gadgets for (k, l)-tight Graphs Do Not Exist
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917473373126656 |
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| author | Chauhan, Archit Gurjar, Rohit Rothmund, Kilian Thierauf, Thomas |
| author_facet | Chauhan, Archit Gurjar, Rohit Rothmund, Kilian Thierauf, Thomas |
| contents | The problem of recognizing (k, l)-tight graphs is a fundamental problem that has close connections to well studied problems like graph rigidity. The problem is better understood for planar graphs as compared to general graphs. For example, deterministic NC-algorithms for the problem are known for planar graphs, but no such algorithm is known for general graphs. A common approach to reduce a graph problem to the planar case is to use planarizing gadgets. Our main contribution is to show that, unconditionally, planarizing gadgets for the problem of recognizing (k, l)-tight graphs do not exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Planarizing Gadgets for (k, l)-tight Graphs Do Not Exist Chauhan, Archit Gurjar, Rohit Rothmund, Kilian Thierauf, Thomas Data Structures and Algorithms Computational Complexity Discrete Mathematics F.2.0 The problem of recognizing (k, l)-tight graphs is a fundamental problem that has close connections to well studied problems like graph rigidity. The problem is better understood for planar graphs as compared to general graphs. For example, deterministic NC-algorithms for the problem are known for planar graphs, but no such algorithm is known for general graphs. A common approach to reduce a graph problem to the planar case is to use planarizing gadgets. Our main contribution is to show that, unconditionally, planarizing gadgets for the problem of recognizing (k, l)-tight graphs do not exist. |
| title | Planarizing Gadgets for (k, l)-tight Graphs Do Not Exist |
| topic | Data Structures and Algorithms Computational Complexity Discrete Mathematics F.2.0 |
| url | https://arxiv.org/abs/2605.08016 |