Planarizing Gadgets for (k, l)-tight Graphs Do Not Exist

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.