The term "Mančinska-Roberson graphs" is used in this work for two graphs introduced by Mančinska and Roberson (2016) in the study of quantum colorings.
The first is a 13-vertex, 24-edge orthogonality graph of the nonzero vectors in
modulo overall sign, also known as the magic cube orthogonality graph (House of Graphs,
Yu and Oh 2012) and the Yu-Oh 13-ray graph (Yu and Oh 2012, Cabello et al. 2016).
The second is the 14-vertex, 37-edge cone graph obtained
by adjoining one apex vertex to the first graph.
The 14-vertex Mančinska-Roberson graph has ordinary chromatic number 5 but quantum chromatic number
4 (Mančinska and Roberson 2016). Lalonde (2025) showed that it is the smallest
graph, by number of vertices, for which these two numbers differ.
The Mančinska-Roberson graphs will be implemented in a future version of the Wolfram Language as GraphData["MancinskaRobersonGraph13"]
and GraphData["MancinskaRobersonGraph14"].
modulo overall sign, also known as the magic cube orthogonality graph (House of Graphs,
Yu and Oh 2012) and the Yu-Oh 13-ray graph (Yu and Oh 2012, Cabello et al. 2016).
The second is the 14-vertex, 37-edge cone graph obtained
by adjoining one apex vertex to the first graph.
