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Counting Independent Sets and Colorings on Random Regular Bipartite Graphs

Authors Chao Liao, Jiabao Lin, Pinyan Lu, Zhenyu Mao

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  • Theory of computation → Design and analysis of algorithms
Keywords
  • Approximate counting
  • Polymer model
  • Hardcore model
  • Coloring
  • Random bipartite graphs

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Abstract

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every Delta-regular bipartite graph if Delta >= 53. In the weighted case, for all sufficiently large integers Delta and weight parameters lambda = Omega~ (1/(Delta)), we also obtain an FPTAS on almost every Delta-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all q >= 3 and sufficiently large integers Delta=Delta(q), there is an FPTAS to count the number of q-colorings on almost every Delta-regular bipartite graph.

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Chao Liao, Jiabao Lin, Pinyan Lu, and Zhenyu Mao. Counting Independent Sets and Colorings on Random Regular Bipartite Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 34:1-34:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.34

Author Details

Chao Liao
  • Shanghai Jiao Tong University, China
Jiabao Lin
  • Shanghai University of Finance and Economics, China
Pinyan Lu
  • Shanghai University of Finance and Economics, China
Zhenyu Mao
  • Shanghai University of Finance and Economics, China

Funding

This work is supported by Innovation Program of Shanghai Municipal Education Commission and the Fundamental Research Funds for the Central Universities.

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