Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena
Document typeConference lecture
PublisherEdicions de la Universitat de Lleida (UdL)
Rights accessRestricted access - publisher's policy
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.
CitationGiménez, 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.