Improve the treewidth-parameterized algorithm running time

Improve the running time of the FPT algorithm for strong odd k-colorability parameterized by treewidth, currently running in O(n^{O(1)}·(k·9^k)^{tw+1}), to narrow the gap with the conditional lower bound of (k−ε)^{tw}n^{O(1)} for every fixed k≥3 and ε>0.

Background

The paper develops a dynamic-programming algorithm for deciding strong odd k-colorability on graphs of treewidth tw. Its stated running time is O(n^{O(1)}·(k·9^k)^{tw+1}).

The paper also proves, under the Strong Exponential Time Hypothesis, that for every k≥3 and ε>0, strong odd k-colorability cannot be solved in time (k−ε)^{tw}n^{O(1)}. The authors explicitly identify closing the gap between these upper and lower bounds as unresolved.