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It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even no conjecture at hand today. Such a conjecture exists for the class of quasi-line graphs. This class of… (More)

The 0/1 primal separation problem is: Given an extreme point ¯ x of a 0/1 polytope P and some point x £ , find an inequality which is tight at ¯ x, violated by x £ and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1… (More)

- Paolo Ventura, Anna Zeppieri, Italo Mazzitelli, Francesca D’Antona
- 1998

We present the results of stellar evolutionary computations to study the sensitivity of lithium depletion in models of mass and metallicity close to solar, and its dependence on the micro – macro physical inputs in the models, like thermo-dynamics, mixing, overshooting and the convective model. We find that even marginal chemical inhomogeneities in stellar… (More)

Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium… (More)

It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even no conjecture at hand today. Such a conjecture exists for the class of quasi-line graphs. This class of… (More)

The 0/1 primal separation problem is: Given an extreme point <i>x</i> of a 0/1 polytope <i>P</i> and some point <i>x*,</i> find an inequality which is tight at <i>x,</i> violated by <i>x*</i> and valid for <i>P</i> or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for… (More)

It is a longstanding open problem whether there exists a polynomial size description of the perfect matching polytope. We give a partial answer to this question by proving the following result. The polyhedron defined by the constraints of the perfect matching polytope which are active at a given perfect matching can be obtained as the projection of a… (More)

We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties. This composition yields counterexamples to a conjecture on the facial structure of ST AB(G) when G is claw-free.

This paper focuses on the outer description of the convex hull of all integer solutions to a given system of linear inequalities. It is shown that if the given system contains lower and upper bounds for the variables , then the convex hull can be produced by iteratively generating so-called mod-2 cuts only. This fact is surprising and might even be… (More)