Drmota, Michael ;
Ramos, Lander ;
Requilé, Clément ;
Rué, Juanjo
Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes
Abstract
We provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in series-parallel graphs (and related graph classes) with n vertices. In particular, our results extend previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988]. We also show that these two parameters converge to a central limit law.
BibTeX - Entry
@InProceedings{drmota_et_al:LIPIcs:2018:8911,
author = {Michael Drmota and Lander Ramos and Cl{\'e}ment Requil{\'e} and Juanjo Ru{\'e}},
title = {{Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes}},
booktitle = {29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
pages = {18:1--18:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-078-1},
ISSN = {1868-8969},
year = {2018},
volume = {110},
editor = {James Allen Fill and Mark Daniel Ward},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8911},
URN = {urn:nbn:de:0030-drops-89117},
doi = {10.4230/LIPIcs.AofA.2018.18},
annote = {Keywords: Asymptotic enumeration, central limit laws, subcritical graph classes, maximal independent set, maximal matching}
}
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Keywords: |
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Asymptotic enumeration, central limit laws, subcritical graph classes, maximal independent set, maximal matching |
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Seminar: |
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29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)
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Issue date: |
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2018 |
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Date of publication: |
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2018 |
2018
