ECCC-Report TR06-044https://eccc.weizmann.ac.il/report/2006/044Comments and Revisions published for TR06-044en-usTue, 28 Mar 2006 00:05:27 +0200
Paper TR06-044
| Inclusion-Exclusion Based Algorithms for Graph Colouring |
Andreas Björklund,
Thore Husfeldt
https://eccc.weizmann.ac.il/report/2006/044We 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 $O(1.2209^n+2.2461^{e^{-\epsilon}n})$.
Tue, 28 Mar 2006 00:05:27 +0200https://eccc.weizmann.ac.il/report/2006/044