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dc.contributor.authorChapuy, G.
dc.contributor.authorPerarnau Llobet, Guillem
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-06-18T07:45:47Z
dc.date.available2020-09-17T00:28:19Z
dc.date.issued2018-09-17
dc.identifier.citationChapuy, G.; Perarnau-Llobet, G. Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture. "Journal of combinatorial theory. Series B", 17 Setembre 2018, vol. 136, p. 44-71.
dc.identifier.issn0095-8956
dc.identifier.urihttp://hdl.handle.net/2117/134647
dc.description.abstractA 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.
dc.format.extent28 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshGraph theory
dc.titleConnectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.identifier.doi10.1016/j.jctb.2018.09.004
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0095895618300856
dc.rights.accessOpen Access
local.identifier.drac24902921
dc.description.versionPostprint (author's final draft)
local.citation.authorChapuy, G.; Perarnau-Llobet, G.
local.citation.publicationNameJournal of combinatorial theory. Series B
local.citation.volume136
local.citation.startingPage44
local.citation.endingPage71


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Attribution-NonCommercial-NoDerivs 3.0 Spain
Llevat que s'hi indiqui el contrari, els continguts d'aquesta obra estan subjectes a la llicència de Creative Commons : Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya