Quantum Mycielski graphs

The classical Mycielski transformation allows for constructing from a given graph a new one with an arbitrarily large chromatic number but preserving the size of the largest clique contained in it. This particular construction and its specific generalizations were widely discussed in graph theory literature. Here we propose an analog of these transformations for quantum graphs and study how they affect the (quantum) chromatic number as well as the clique numbers associated with them.