Strong spatial mixing for list coloring of graphs
Name
Gamarnik_Strong spatial.pdf
Size
148.27 KB
Format
Adobe PDF
Checksum (MD5)
8ebe937f7ed2a1f3245337e0c8329e22
Author(s)
Gamarnik, David
Katz, Dmitriy
Misra, Sidhant
Alternative Title
Strong spatial mixing of list coloring of graphs
Date Issued
October 2013
Journal
Random Structures & Algorithms
Publisher
Wiley Blackwell
Citation
Gamarnik, David, Dmitriy Katz, and Sidhant Misra. “Strong Spatial Mixing of List Coloring of Graphs.” Random Structures & Algorithms 46, no. 4 (October 11, 2013): 599–613.
Version
Original manuscript
Abstract
The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise known to be #P hard. In the context of coloring, strong spatial mixing has been established for Kelly trees in (Ge and Stefankovic, arXiv:1102.2886v3 (2011)) when q ≥ α[superscript *] Δ + 1 where q the number of colors, Δ is the degree and α[superscript *] is the unique solution to xe[superscript -1/x] = 1. It has also been established in (Goldberg et al., SICOMP 35 (2005) 486–517) for bounded degree lattice graphs whenever q ≥ α[superscript *] Δ - β for some constant β, where Δ is the maximum vertex degree of the graph. We establish strong spatial mixing for a more general problem, namely list coloring, for arbitrary bounded degree triangle-free graphs. Our results hold for any α > α[superscript *] whenever the size of the list of each vertex v is at least αΔ(v) + β where Δ(v) is the degree of vertex v and β is a constant that only depends on α. The result is obtained by proving the decay of correlations of marginal probabilities associated with graph nodes measured using a suitably chosen error function.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/rsa.20518
