Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph

The minimum rank of a graph G is the ranks all symmetric adjacency matrices G. We present new combinatorial bound for an arbitrary based on enumerating certain subsets vertices satisfying matroid theoretic properties. also some computational and theoretical challenges associated with computing rank. This includes conjecture that this actually holds equality graphs. History: “Challenge” paper was invited by Editor in Chief topics raised author at his plenary address 2022 INFORMS Computing Society Conference Tampa, Florida. Funding: work supported National Science Foundation [Grant DMS-1720225]. Supplemental Material: online appendix available https://doi.org/10.1287/ijoc.2022.1219 .