Planarizing Gadgets for (k, l)-tight Graphs Do Not Exist
Data Structures and Algorithms
2026-05-11 v1 Computational Complexity
Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.2605.08016,
title = {Planarizing Gadgets for (k, l)-tight Graphs Do Not Exist},
author = {Archit Chauhan and Rohit Gurjar and Kilian Rothmund and Thomas Thierauf},
journal= {arXiv preprint arXiv:2605.08016},
year = {2026}
}