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Title:	Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture
Author:	Chapuy, G.; Perarnau Llobet, Guillem
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
Abstract:	A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, that says that if is any bridge-addable class of graphs on n vertices, and is taken uniformly at random from , then is connected with probability at least , when n tends to infinity. This lower bound is asymptotically best possible since it is reached for forests. Our proof uses a “local double counting” strategy that may be of independent interest, and that enables us to compare the size of two sets of combinatorial objects by solving a related multivariate optimization problem. In our case, the optimization problem deals with partition functions of trees relative to a supermultiplicative functional.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Graph theory -Grafs, Teoria de
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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