The Delta Conjecture for maximum nullity of graphs

Let $G$ be a simple graph, and let $\delta(G)$ denote its minimum degree. The maximum nullity $\mathrm{M}(G)$ is the greatest nullity among matrices associated with $G$ in the maximum nullity problem. Delta Conjecture. For every simple graph $G$,

$$\delta(G) \le \mathrm{M}(G).$$

The conjecture arose in combinatorial matrix theory and is a lower bound on maximum nullity. It is known for all bipartite graphs and for complements of bipartite graphs, but the source does not report a complete resolution.