Results 11 to 20 of about 3,648 (134)
Chain polynomials and Tutte polynomials
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lorenzo Traldi
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Weighted Tutte–Grothendieck Polynomials of Graphs
Graphs and Combinatorics, 2023 In this paper, we introduce the concept of the weighted (harmonic) chromatic polynomials of graphs and discuss some of its properties. We also present the notion of the weighted (harmonic) Tutte--Grothendieck polynomials of graphs and give a generalization of the recipe theorem between the harmonic Tutte--Grothendieck polynomials graphs and the ...
Himadri Shekhar Chakraborty +2 more
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Graph polynomials derived from Tutte–Martin polynomials
Discrete Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Colored Tutte polynomials and composite knots [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Surveying the results of three recent papers and some currently ongoing research, we show how a generalization of Brylawski's tensor product formula to colored graphs may be used to compute the Jones polynomial of some fairly complicated knots and, in ...
Gábor Hetyei +2 more
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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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Growing uniform planar maps face by face
Random Structures &Algorithms, Volume 63, Issue 4, Page 942-967, December 2023., 2023 Abstract We provide “growth schemes” for inductively generating uniform random 2p$$ 2p $$‐angulations of the sphere with n$$ n $$ faces, as well as uniform random simple triangulations of the sphere with 2n$$ 2n $$ faces. In the case of 2p$$ 2p $$‐angulations, we provide a way to insert a new face at a random location in a uniform 2p$$ 2p $$‐angulation
Alessandra Caraceni, Alexandre Stauffer
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Geometric bijections between spanning subgraphs and orientations of a graph
Journal of the London Mathematical Society, Volume 108, Issue 3, Page 1082-1120, September 2023., 2023 Abstract Let G$G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy‐to‐describe bijections between spanning trees of G$G$ and (σ,σ∗)$(\sigma ,\sigma ^*)$‐compatible orientations, where the (σ,σ∗)$(\sigma ,\sigma ^*)$‐compatible orientations are the representatives of equivalence classes of orientations
Changxin Ding
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Advances in Mathematics, 2022 The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polymatroids, as a two-variable polynomial. Our definition is related to previous works of Cameron and Fink and of K lm n and Postnikov.
Bernardi, Olivier +2 more
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On sufficient conditions for spanning structures in dense graphs
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 709-791, September 2023., 2023 Abstract We study structural conditions in dense graphs that guarantee the existence of vertex‐spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and, excluding the bipartite case, contains an odd cycle.
Richard Lang +1 more
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