Results 51 to 60 of about 6,580 (165)
Formulas for the computation of the Tutte polynomial of graphs with parallel classes
Electronic Journal of Graph Theory and Applications, 2018 We give some reduction formulas for computing the Tutte polynomial of any graph with parallel classes. Several examples are given to illustrate our results.
Eunice Mphako-Banda, Julian A. Allagan
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Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of a matroid $M$ over a commutative ring $R$, assigning to every subset of the ground set an $R$-module according to some axioms. When $R$ is a field, we recover matroids.
Alex Fink, Luca Moci
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The Tutte-Grothendieck group of a convergent alphabetic rewriting system [PDF]
, 2011 The two operations, deletion and contraction of an edge, on multigraphs directly lead to the Tutte polynomial which satisfies a universal problem. As observed by Brylawski in terms of order relations, these operations may be interpreted as a particular ...
Poinsot, Laurent
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The Arithmetic Tutte polynomial of two matrices associated to Trees
Special Matrices, 2018 Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B. +1 more
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Flows on Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Given a graph $G$, the number of nowhere-zero $\mathbb{Z}_q$-flows $\phi _G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\mathbb{Z} _q$-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove ...
Matthias Beck, Yvonne Kemper
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Quasi-tree expansion for the Bollob\'as-Riordan-Tutte polynomial
, 2011 Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. The Bollob\'as-Riordan-Tutte polynomial is a three-variable polynomial that extends the Tutte polynomial to oriented ribbon graphs.
Champanerkar, Abhijit +2 more
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Spanning forests in regular planar maps (conference version) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We address the enumeration of $p$-valent planar maps equipped with a spanning forest, with a weight $z$ per face and a weight $u$ per component of the forest.
Mireille Bousquet-Mélou +1 more
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Bipartition Polynomials, the Ising Model, and Domination in Graphs
Discussiones Mathematicae Graph Theory, 2015 This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph.
Dod Markus +3 more
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Chain polynomials and Tutte polynomials
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Discrete & Computational GeometryAbstract We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by Berget, Eur, Spink and Tseng to the product space $${{\mathbb {P}}}^n \times {{\mathbb {P}}}^n$$
Mario Bauer +4 more
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