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.

翻译：识别 (k, l)-紧致图的问题是一个基础性问题，与图刚性等深入研究的问题密切相关。相较于一般图，该问题在平面图上的理解更为透彻。例如，针对平面图已有确定性的NC算法，而一般图则尚未发现此类算法。将图问题简化为平面情形的常用方法是采用平面化装置。我们的主要贡献在于证明：对于识别 (k, l)-紧致图的问题，平面化装置无条件地不存在。