TR06-044 Authors: Andreas Björklund, Thore Husfeldt

Publication: 28th March 2006 00:05

Downloads: 2366

Keywords:

We present a deterministic algorithm producing the number of

$k$-colourings of a graph on $n$ vertices in time

$2^nn^{O(1)}$.

We also show that the chromatic number can be found by a

polynomial space algorithm running in time $O(2.2461^n)$.

Finally, we present a family of polynomial space approximation

algorithms that find a number between $\chi(G)$ and

$(1+\epsilon)\chi(G)$ in time $O(1.2209^n+2.2461^{e^{-\epsilon}n})$.