  In this work, we present a complete hybrid classical-quantum algorithm
involving a quantum sampler based on neutral atom platforms. This approach is
inspired by classical column generation frameworks developed in the field of
Operations Research and shows how quantum procedures can assist classical
solvers in addressing hard combinatorial problems. We benchmark our method on
the Minimum Vertex Coloring problem and show that the proposed hybrid
quantum-classical column generation algorithm can yield good solutions in
relatively few iterations. We compare our results with state-of-the-art
classical and quantum approaches.
