Improved bounds for perfect sampling of k-colorings in graphs

@article{Bhandari2019ImprovedBF,
  title={Improved bounds for perfect sampling of k-colorings in graphs},
  author={Siddharth Bhandari and Sayantan Chakraborty},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  year={2019}
}
  • Siddharth Bhandari, Sayantan Chakraborty
  • Published 2019
  • Computer Science, Mathematics
  • Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
  • We present a randomized algorithm that takes as input an undirected n-vertex graph G with maximum degree Δ and an integer k > 3Δ, 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; the expected running time of the algorithm is poly(k,n)=O(nΔ2· log(k)). This improves upon a result of Huber (STOC 1998) who obtained a polynomial time perfect sampling algorithm for k>Δ2+2Δ. Prior to our work, no algorithm with… CONTINUE READING

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