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

arXiv: https://arxiv.org/abs/2108.09061 · HTML: https://mlsanity.com/paper/2108.09061/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2021.

## Built on by (most cited first, 2 of 2)

- [What is Cognitive Computing? An Architecture and State of The Art](https://mlsanity.com/paper/2301.00882/) (2023)
- [Deep k-grouping: An Unsupervised Learning Framework for Combinatorial Optimization on Graphs and Hypergraphs](https://mlsanity.com/paper/2505.20972/) (2025)

## Abstract (arXiv)

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(2n) for k≥ 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 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.