Results 31 to 40 of about 156 (150)
Journal of Graph Theory, Volume 101, Issue 2, Page 210-225, October 2022., 2022 Abstract In this article, we investigate the structure of uniformly k $k$‐connected and uniformly k $k$‐edge‐connected graphs. Whereas both types have previously been studied independent of each other, we analyze relations between these two classes. We prove that any uniformly k $k$‐connected graph is also uniformly k $k$‐edge‐connected for k≤3 $k\le 3$
Frank Göring +2 more
wiley +1 more source
Evaluations of Topological Tutte Polynomials [PDF]
Combinatorics, Probability and Computing, 2014 We find new properties of the topological transition polynomial of embedded graphs, Q(G). We use these properties to explain the striking similarities between certain evaluations of Bollobás and Riordan's ribbon graph polynomial, R(G), and the topological Penrose polynomial, P(G).
Joanna A. Ellis-Monaghan, Iain Moffatt
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Arithmetic matroids and Tutte polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce the notion of arithmetic matroid, whose main example is provided by a list of elements in a finitely generated abelian group. We study the representability of its dual, and, guided by the geometry of toric arrangements, we give a ...
Michele D'Adderio, Luca Moci
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Enumerating conjugacy classes of graphical groups over finite fields
Bulletin of the London Mathematical Society, Volume 54, Issue 5, Page 1923-1943, October 2022., 2022 Abstract Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to their sizes.
Tobias Rossmann
wiley +1 more source
Cumulants of the q-semicircular law, Tutte polynomials, and heaps [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 The q-semicircular law as introduced by Bożejko and Speicher interpolates between the Gaussian law and the semicircular law, and its moments have a combinatorial interpretation in terms of matchings and crossings.
Matthieu Josuat-Vergès
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TinyAD: Automatic Differentiation in Geometry Processing Made Simple
Computer Graphics Forum, Volume 41, Issue 5, Page 113-124, August 2022., 2022 Abstract Non‐linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second‐order derivatives are required.
P. Schmidt +4 more
wiley +1 more source
Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A = k[x1, …, xn]. Besides, we compare graded linearity with componentwise linearity in general.
Mohammad Reza-Rahmati +2 more
wiley +1 more source
Combinatorics, Probability and Computing, 2018 We follow the example of Tutte in his construction of the dichromate of a graph (i.e. the Tutte polynomial) as a unification of the chromatic polynomial and the flow polynomial in order to construct a new polynomial invariant of maps (graphs embedded in orientable surfaces). We call this the surface Tutte polynomial.
Vena, Lluis +4 more
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K-classes for matroids and equivariant localization [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial.
Alex Fink, David Speyer
doaj +1 more source
The Incidence Hopf Algebra of Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions.
Brandon Humpert, Jeremy L. Martin
doaj +1 more source