Strong spatial mixing of $q$-colorings on Bethe lattices

Details Strong spatial mixing of $q$-colorings on Bethe lattices Strong spatial mixing of $q$-colorings on Bethe lattices

2011-02-14

arxiv.org/abs/1102.2886v3

Mathematics

Probability

We correct a mistake in our arguments and use $\ell_1$-norm instead of $\ell_\infty$-norm

Scientific paper

We investigate the problem of strong spatial mixing of $q$-colorings on Bethe
lattices. By analyzing the sum-product algorithm we establish the strong
spatial mixing of $q$-colorings on $(b+1)$-regular Bethe lattices, for $q \geq
1+\lceil 1.764b \rceil$. We also establish the strong spatial mixing of
$q$-colorings on binary trees, for $q=4$.

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