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On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs

100%

Avrachenkov K., Ejov V., Filar J.

Banach Center Publications

2006

tom 71

nr 1

29-38

In this note we consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter ε. Recently, the theory of Gröbner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in ε in a neighbourhood of ε = 0. In this paper we show that the determination of the branching order and the order of the pole (if any) of these Puiseux series can be achieved by invoking a classical technique known as the "Newton's polygon" and using it in conjunction with the Gröbner bases techniques.

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A conjecture on the prevalence of cubic bridge graphs

100%

Filar J., Haythorpe M., Nguyen G.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 1

175-179

Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.

Ograniczanie wyników

1 Banach Center Publications

1 Discussiones Mathematicae Graph Theory

2 Filar J.

1 Avrachenkov K.

1 Ejov V.

1 Haythorpe M.

1 Nguyen G.

1 2010

1 2006

Wyniki wyszukiwania

On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs

A conjecture on the prevalence of cubic bridge graphs