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: https://drops.dagstuhl.de/opus/volltexte/2019/11249/
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 | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 17.09.2019 |
