منابع مشابه
Homomorphism and Sigma Polynomials
By establishing a connection between the sigma polynomial and the homomorphism polynomial, many of the proofs for computing the sigma polynmial are simplified, the homomorphism polynomial can be identified for several new classes of graphs, and progress can be made on identifying homomorphism polynomials.
متن کاملHomomorphism Polynomials Complete for VP
The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant of a matrix of polynomially bounded size. Strikingly, this restatement does not me...
متن کاملA Dichotomy Theorem for Homomorphism Polynomials
In the present paper we show a dichotomy theorem for the complexity of polynomial evaluation. We associate to each graph H a polynomial that encodes all graphs of a fixed size homomorphic to H . We show that this family is computable by arithmetic circuits in constant depth if H has a loop or no edge and that it is hard otherwise (i.e., complete for VNP, the arithmetic class related to #P ). We...
متن کاملTwisted Alexander polynomials and surjectivity of a group homomorphism
If ϕ : G → G ′ is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G ′. As an application, we show non-existence of surjective homomorphism between certain knot groups.
متن کاملDichotomy Theorems for Homomorphism Polynomials of Graph Classes
In this paper, we will show dichotomy theorems for the computation of polynomials corresponding to evaluation of graph homomorphisms in Valiant’s model. We are given a fixed graph H and want to find all graphs, from some graph class, homomorphic to this H. These graphs will be encoded by a family of polynomials. We give dichotomies for the polynomials for cycles, cliques, trees, outerplanar gra...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1995
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171295000834