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≥1+⌈1.764b⌉. We also establish the strong spatial mixing of q-colorings on binary trees, for q=4.
@article{arxiv.1102.2886,
title = {Strong spatial mixing of $q$-colorings on Bethe lattices},
author = {Qi Ge and Daniel Stefankovic},
journal= {arXiv preprint arXiv:1102.2886},
year = {2011}
}
Comments
We correct a mistake in our arguments and use $\ell_1$-norm instead of $\ell_\infty$-norm