# A Grover search-based algorithm for the list coloring problem

Published in *IEEE Transactions on Quantum Engineering*, 2022

Recommended citation: Mukherjee, Sayan. "A Grover search-based algorithm for the list coloring problem." *IEEE Transactions on Quantum Engineering* Volume 3 (2022).

Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more general question: given a *list* of available colors for each vertex in a graph, does it admit a proper coloring? We propose a hybrid classical-quantum algorithm based on Grover search to quadratically speed up exhaustive search. Our algorithm loses in complexity to classical ones in specific restricted cases, but improves exhaustive search for cases where the lists and graphs considered are arbitrary in nature.

DOI: 10.1109/TQE.2022.3151137