On the sphericity of scaling limits of random planar quadrangulations.
Miermont, Grégory (2008)
Electronic Communications in Probability [electronic only]
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Miermont, Grégory (2008)
Electronic Communications in Probability [electronic only]
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Jeff Cheeger, Bruce Kleiner (2015)
Analysis and Geometry in Metric Spaces
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We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as...
Babilon, Robert, Matoušek, Jiří, Maxová, Jana, Valtr, Pavel (2003)
Journal of Graph Algorithms and Applications
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Pálvölgyi, Dömötör (2009)
Acta Universitatis Sapientiae. Mathematica
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Andreica, Mugurel Ionuţ, Ţăpuş, Nicolae (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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Vetrík, T. (2007)
Acta Mathematica Universitatis Comenianae. New Series
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Noskov, Gennady A. (2000)
Geometry & Topology
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Rosário Fernandes (2015)
Special Matrices
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The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2....
Cabello, Sergio, Lukšič, Primož (2011)
The Electronic Journal of Combinatorics [electronic only]
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Bohdan Zelinka (1992)
Archivum Mathematicum
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Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances.