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Stable sets for $(P₆,K_{2,3})$-free graphs

100%

Mosca R.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 3

387-401

The Maximum Stable Set (MS) problem is a well known NP-hard problem. However different graph classes for which MS can be efficiently solved have been detected and the augmenting graph technique seems to be a fruitful tool to this aim. In this paper we apply a recent characterization of minimal augmenting graphs [22] to prove that MS can be solved for $(P₆,K_{2,3})$-free graphs in polynomial time, extending some known results.

Isoperimetric and Stable Sets for Log-Concave Perturbations of Gaussian Measures

88%

Rosales C.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

Let be an open half-space or slab in ℝn+1 endowed with a perturbation of the Gaussian measure of the form f (p) := exp(ω(p) − c|p|2), where c > 0 and ω is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization of half-spaces parallel or perpendicular to ∂ Ω as the unique stable sets with small singular set and null weighted capacity. Our methods also apply for = ℝn+1, which produces in particular the classification of stable sets in Gauss space and a new proof of the Gaussian isoperimetric inequality. Finally, we use optimal transport to study the weighted minimizers when the perturbation term ω is concave and possibly non-smooth.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Discussiones Mathematicae Graph Theory

1 Mosca R.

1 Rosales C.

1 2014

1 2012

Wyniki wyszukiwania

Stable sets for $(P₆,K_{2,3})$-free graphs

Isoperimetric and Stable Sets for Log-Concave Perturbations of Gaussian Measures