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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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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.

Cite AsGet BibTex

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

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.

Subject Classification

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

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