Current state of polynomial-space exact graph coloring

The fastest algorithm I could find that finds the chromatic number of an undirected simple graph exactly in only polynomial-space is "Faster Graph Coloring in Polynomial Space" by Gaspers and Lee (DOI: 10.1007/978-3-319-62389-4_31). It's running time is $$O(2.2356^n)$$.

However that's from 2016/2017, so I'm wondering whether there are any new relevant developments.

The mentioned algorithm is based on a procedure for counting the number of independent sets of a graph, meaning that new developments in that area are possibly relevant, too.

• for a polynomial space (as in the title of the question), just enumerate all different coloring options until you find a correct one. Jan 5 at 20:01
• @nirshahar Are you trolling? That's a lot slower than the algorithm from 2017. Jan 5 at 20:03
• Sorry, I might have misunderstood your question. Do you ask for an algorithm with the least space used? Or poly-space with the least time? Jan 5 at 21:55
• @nirshahar Poly-space with the least time. Jan 6 at 6:37