Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Volume Bounds for Trivalent Planar Graphs
View through CrossRef
This paper studies the volumes of hyperbolic planar trivalent graphs. The connection between fully augmented links and trivalent planar graphs allows us to apply previous work on knots and links to this setting. Exact volume bounds for graphs with up to 12 vertices are calculated. Purcell’s sharp lower bound for the volumes of fully augmented links translates directly to a lower bound for trivalent graphs. Moreover, a natural cell decomposition on trivalent graphs allows us to interpret upper bounds for link volumes in the graph theoretic setting. This is done for both the Agol Thurston tetrahedral upper bound and Adams' bipyramidal upper bound. An infinite family of graphs, inspired by Agol-Thurston’s infinite chain link fence, proves these bounds are asymptotically equivalent.
California State University, Office of the Chancellor
Title: Volume Bounds for Trivalent Planar Graphs
Description:
This paper studies the volumes of hyperbolic planar trivalent graphs.
The connection between fully augmented links and trivalent planar graphs allows us to apply previous work on knots and links to this setting.
Exact volume bounds for graphs with up to 12 vertices are calculated.
Purcell’s sharp lower bound for the volumes of fully augmented links translates directly to a lower bound for trivalent graphs.
Moreover, a natural cell decomposition on trivalent graphs allows us to interpret upper bounds for link volumes in the graph theoretic setting.
This is done for both the Agol Thurston tetrahedral upper bound and Adams' bipyramidal upper bound.
An infinite family of graphs, inspired by Agol-Thurston’s infinite chain link fence, proves these bounds are asymptotically equivalent.
Related Results
Indeterminate solitary vertebral lesions on planar scintigraphy
Indeterminate solitary vertebral lesions on planar scintigraphy
Summary
Objective: This study aims to evaluate the added value of hybrid SPECT-CT in differential diagnosis of indeterminate solitary vertebral lesion (SVL) on planar sci...
Subexponential lower bounds for f-ergodic Markov processes
Subexponential lower bounds for f-ergodic Markov processes
AbstractWe provide a criterion for establishing lower bounds on the rate of convergence in f-variation of a continuous-time ergodic Markov process to its invariant measure. The cri...
On Tuza's conjecture in even co-chain graphs
On Tuza's conjecture in even co-chain graphs
In 1981, Tuza conjectured that the cardinality of a minimum set of edges that intersects every triangle of a graph is at most twice the cardinality of a maximum set of edge-disjoin...
Twilight graphs
Twilight graphs
AbstractThis paper deals primarily with countable, simple, connected graphs and the following two conditions which are trivially satisfied if the graphs are finite:(a) there is an ...
Model-checking ecological state-transition graphs
Model-checking ecological state-transition graphs
AbstractModel-checking is a methodology developed in computer science to automatically assess the dynamics of discrete systems, by checking if a system modelled as a state-transiti...
Solving minimum K‐cardinality cut problems in planar graphs
Solving minimum K‐cardinality cut problems in planar graphs
AbstractThe present work tackles a recent problem in the class of cardinality constrained combinatorial optimization problems for the planar graph case: the minimum k‐cardinality c...
Rigorous Asymptotic Perturbation Bounds for Hermitian Matrix Eigendecompositions
Rigorous Asymptotic Perturbation Bounds for Hermitian Matrix Eigendecompositions
In this paper, we present rigorous asymptotic componentwise perturbation bounds for regular Hermitian indefinite matrix eigendecompositions, obtained by the method of the splitting...