Matroid Steiner problems, the Tutte polynomial and network reliability
نویسندگان
چکیده
منابع مشابه
The Tutte polynomial of a ported matroid
Las Vergnas’ generalizations of the Tutte polynomial are studied as follows. The theory of Tutte-Grothendieck matroid invariantsfis modified so the Tutte decomposition ,f(M) =f(M\e) +f( M/e) is applied only when e $ P (and e is neither a loop nor an isthmus) where P is a distinguished set of points called ports. The resulting “P-ported” Tutte polynomial tp has variables I, w; q,, qZ, . . . . qm...
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We solve in the affirmative a conjecture of Brylawski, namely that the Tutte polynomial of a connected matroid is irreducible over the integers. If M is a matroid over a set E, then its Tutte polynomial is defined as T(M; x, y)= C A ı E (x − 1) r(E) − r(A) (y − 1) | A | − r(A) , where r(A) is the rank of A in M. This polynomial is an important invariant as it contains much information on the ma...
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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.
متن کاملApproximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials
We consider the problem of approximating certain combinatorial polynomials. First, we consider the problem of approximating the Tutte polynomial of a binary matroid with parameters q ≥ 2 and γ. (Relative to the classical (x, y) parameterisation, q = (x− 1)(y− 1) and γ = y− 1.) A graph is a special case of a binary matroid, so earlier work by the authors shows inapproximability (subject to certa...
متن کاملOn the evaluation at (j, j2) of the Tutte polynomial of a ternary matroid
F. Jaeger has shown that up to a ± sign the evaluation at ( j, j2) of the Tutte polynomial of a ternary matroid can be expressed in terms of the dimension of the bicycle space of a representation over G F(3). We give a short algebraic proof of this result, which moreover yields the exact value of ±, a problem left open in Jaeger’s paper. It follows that the computation of t( j, j2) is of polyno...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1989
ISSN: 0095-8956
DOI: 10.1016/0095-8956(89)90062-2