A faster algorithm for independent cut

Abstract

The previously fastest algorithm for deciding the existence of an independent cut had a runtime of $O^{*}(1.{4423}^n)$, where $n$ is the order of the input graph. We improve this to $O^{*}(1.{4143}^n)$. In fact, we prove a runtime of $O^{*}\left(2^{(\frac{1}{2}-{\alpha }_{\Delta })n}\right)$ on graphs of order $n$ and maximum degree at most $\Delta$, where ${\alpha }_{\Delta }=\frac{1}{2+4\lfloor \frac{\Delta }{2}\rfloor }$. Furthermore, we show that the problem is fixed-parameter tractable on graphs of order $n$ and minimum degree at least $\beta n$ for some $\beta >\frac{1}{2}$, where $\beta$ is the parameter.