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dc.contributor.authorAtserias, Albert
dc.contributor.authorKreutzer, Stephan
dc.contributor.authorNoy Serrano, Marcos
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2018-11-16T09:21:09Z
dc.date.available2018-11-16T09:21:09Z
dc.date.issued2018
dc.identifier.citationAtserias, A., Kreutzer, S., Noy, M. On zero-one and convergence laws for graphs embeddable on a fixed surface. A: International Colloquium on Automata, Languages, and Programming. "45th International Colloquium on Automata, Languages, and Programming (ICALP 2018): July 9-13, 2018, Prague, Czech Republic". Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 1-14.
dc.identifier.isbn978-3-95977-076-7
dc.identifier.urihttp://hdl.handle.net/2117/124541
dc.description.abstractWe show that for no surface except for the plane does monadic second-order logic (MSO) have a zero-one-law - and not even a convergence law - on the class of (connected) graphs embeddable on the surface. In addition we show that every rational in [0,1] is the limiting probability of some MSO formula. This strongly refutes a conjecture by Heinig et al. (2014) who proved a convergence law for planar graphs, and a zero-one law for connected planar graphs, and also identified the so-called gaps of [0,1]: the subintervals that are not limiting probabilities of any MSO formula. The proof relies on a combination of methods from structural graph theory, especially large face-width embeddings of graphs on surfaces, analytic combinatorics, and finite model theory, and several parts of the proof may be of independent interest. In particular, we identify precisely the properties that make the zero-one law work on planar graphs but fail for every other surface.
dc.format.extent14 p.
dc.language.isoeng
dc.publisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
dc.rightsAttribution 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica
dc.subject.lcshGraphic methods
dc.subject.lcshComputer science -- Mathematics
dc.subject.otherConvergence law
dc.subject.otherMonadic second-order logic
dc.subject.otherRandom graphs
dc.subject.otherTopological graph theory
dc.subject.otherZero-one law
dc.subject.otherAutomata theory
dc.subject.otherComputer circuits
dc.titleOn zero-one and convergence laws for graphs embeddable on a fixed surface
dc.typeConference report
dc.subject.lemacMètodes gràfics
dc.subject.lemacInformàtica -- Matemàtica
dc.contributor.groupUniversitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals
dc.contributor.groupUniversitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.identifier.doi10.4230/LIPIcs.ICALP.2018.116
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://drops.dagstuhl.de/opus/volltexte/2018/9120/
dc.rights.accessOpen Access
drac.iddocument23444382
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020-648276-AUTAR
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/1PE/MTM2014-54745-P
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/MDM-2014-0445
upcommons.citation.authorAtserias, A., Kreutzer, S., Noy, M.
upcommons.citation.contributorInternational Colloquium on Automata, Languages, and Programming
upcommons.citation.pubplaceWadern
upcommons.citation.publishedtrue
upcommons.citation.publicationName45th International Colloquium on Automata, Languages, and Programming (ICALP 2018): July 9-13, 2018, Prague, Czech Republic
upcommons.citation.startingPage1
upcommons.citation.endingPage14


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