License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.34
URN: urn:nbn:de:0030-drops-112498
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11249/
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Liao, Chao ; Lin, Jiabao ; Lu, Pinyan ; Mao, Zhenyu

Counting Independent Sets and Colorings on Random Regular 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.

BibTeX - Entry

@InProceedings{liao_et_al:LIPIcs:2019:11249,
  author =	{Chao Liao and Jiabao Lin and Pinyan Lu and Zhenyu Mao},
  title =	{{Counting Independent Sets and Colorings on Random Regular Bipartite Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{34:1--34:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11249},
  URN =		{urn:nbn:de:0030-drops-112498},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.34},
  annote =	{Keywords: Approximate counting, Polymer model, Hardcore model, Coloring, Random bipartite graphs}
}

Keywords: Approximate counting, Polymer model, Hardcore model, Coloring, Random bipartite graphs
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue Date: 2019
Date of publication: 17.09.2019

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