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Electronic Colloquium on Computational Complexity

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Reports tagged with Graph colouring:
TR06-044 | 24th January 2006
Andreas Björklund, Thore Husfeldt

Inclusion-Exclusion Based Algorithms for Graph Colouring

We present a deterministic algorithm producing the number of
$k$-colourings of a graph on $n$ vertices in time
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 ... more >>>

TR19-164 | 6th November 2019
Siddharth Bhandari, Sayantan Chakraborty

Improved bounds for perfect sampling of $k$-colorings in graphs

Revisions: 1

We present a randomized algorithm that takes as input an undirected $n$-vertex graph $G$ with maximum degree $\Delta$ and an integer $k > 3\Delta$, and returns a random proper $k$-coloring of $G$. The
distribution of the coloring is perfectly uniform over the set of all proper $k$-colorings; ... more >>>

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