A Characterization of the Tutte Polynomial via Combinatorial Embeddings
نویسندگان
چکیده
منابع مشابه
A characterization of the Tutte polynomial via combinatorial embeddings
We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of spanning trees counted according to activities. Tutte’s notion of activity requires a choice of a linear order on the edge set (though the generating function of the activities is, in fact, independent...
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The Tutte polynomial is one of the most important and most useful invariants of a graph. It was discovered as a two variable generalization of the chromatic polynomial [15, 16], and has been studied in literally hundreds of papers, in part due to its connections to various fields ranging from Enumerative Combinatorics to Knot Theory, from Statistical Physics to Computer Science. We refer the re...
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The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.
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For any graph G with n edges, the spanning subgraphs and the orientations of G are both counted by the evaluation TG(2, 2) = 2 n of its Tutte polynomial. We define a bijection Φ between spanning subgraphs and orientations and explore its enumerative consequences regarding the Tutte polynomial. The bijection Φ is closely related to a recent characterization of the Tutte polynomial relying on a c...
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This is a close approximation to the content of my lecture. After a brief survey of well known properties, I present some new interpretations relating to random graphs, lattice point enumeration, and chip firing games. I then examine complexity issues and concentrate in particular, on the existence of randomized approximation schemes. © 1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 210–...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2008
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-008-0343-4