Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/117883

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.contributor.author	Giménez Llach, Omer
dc.contributor.author	Noy Serrano, Marcos
dc.contributor.author	Rué Perna, Juan José
dc.date	2008
dc.identifier.citation	Giménez, O., Noy, M., Rue, J. Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena. A: Jornadas de Matemática Discreta y Algorítmica. "Jornadas de Matemática Discreta y Algorítmica: 6es, 2008, Lleida, Espanya". Edicions de la Universitat de Lleida (UdL), 2008, p. 369-377.
dc.identifier.citation	978-84-8409-263-6
dc.identifier.citation	L-1.014-2008
dc.identifier.uri	http://hdl.handle.net/2117/117883
dc.language.iso	eng
dc.publisher	Edicions de la Universitat de Lleida (UdL)
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Combinatorial analysis
dc.subject	Graph theory
dc.subject	analytic combinatorics
dc.subject	asymptotic enumeration
dc.subject	limit laws
dc.subject	random graph
dc.subject	planar graph
dc.subject	Grafs, Teoria de
dc.subject	Anàlisi combinatòria
dc.title	Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/conferenceObject
dc.description.abstract	Consider a family T of 3-connected graphs, and let G be the class of graphs whose 3-connected components are graphs in T . We present a general framework for analyzing such graphs classes based on singularity analysis of generating functions. This generalizes previously studied cases such as planar graphs and seriesparallel graphs. We provide a general theorem for the asymptotic number of graphs in G, based on the singularities of the exponential generating function associated to T . We derive limit laws for the number of connected components, for the number of edges and for the number of 2-connected components. At last, for some classes under study we show the existence of critical phenomena as the edge density in the class varies.

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