Results 11 to 20 of about 495 (157)
A study about the Tutte polynomials of benzenoid chains
Topological Algebra and its Applications, 2017 The Tutte polynomials for signed graphs were introduced by Kauffman. In 2012, Fath-Tabar, Gholam-Rezaeı and Ashrafı presented a formula for computing Tutte polynomial of a benzenoid chain. From this point on, we have also calculated the Tutte polynomials
Sahin Abdulgani
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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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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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Some inequalities for the Tutte polynomial
European Journal of Combinatorics, 2011 17 ...
Laura Chávez-Lomelí +3 more
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Tutte Polynomials and Graph Symmetries
Symmetry, 2022 The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts
Nafaa Chbili +3 more
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Simulating quantum computations with Tutte polynomials
npj Quantum Information, 2021 We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic matroids.
Ryan L. Mann
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Fourientations and the Tutte polynomial [PDF]
Research in the Mathematical Sciences, 2017 A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we investigate properties of cuts and cycles in fourientations which give trivariate generating functions that are generalized
Backman, Spencer, Hopkins, Sam
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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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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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