We determine the order of growth of the worst-case number of perfect subgraphs needed to cover an n-vertex graph.

John Harris: The only traits it would be morally problematic to induce are those that would be harmful to the individual or to others. It wouldn't be morally problematic if a woman had a boy rather than a girl, or a child with a particular skin or eye colour or high intelligence. No one has a reason to bemoan the birth of such a child. Nor would the child have grounds for complaint. On the othe...

Among the powerful barriers to making progress in patient safety is an attitude of complacency induced by the rarity of serious events and the general human bias toward assuming that things will work as they are supposed to. Although the overall incidence figures for accidental injuries and deaths in healthcare are horrendous—more than 1 million preventable injuries and 44 000–98 000 preventabl...

A connected graph G is called t-perfect if its stable set polytope is determined by the non-negativity, edge and odd-cycle inequalities. Moreover, G is called strongly t-perfect if this system is totally dual integral. It is an open problem whether t-perfection is equivalent to strong t-perfection. We prove the equivalence for the class of claw-free graphs.

High-resolution X-ray diffractometry, absolute integrated intensity ( ) measurements, diffuse X-ray scattering (DXS) and infrared (IR) absorption techniques were used to investigate the in ̄uence of oxygen on the structural perfection of high purity (resistivity of the order of 4 k cm) ̄oat zone (FZ) grown (111) silicon single crystals. A multicrystal diffractometer set in …‡;ÿ;ÿ;‡† geometry, wit...

It is a well-known fact that stable semantics might not provide any extensions for some given abstract argumentation framework. Arguably such frameworks might be considered futile, at least with respect to stable semantics. We propagate σ -perfection stating that for a given argumentation graph all induced subgraphs provide σ -extensions. We discuss perfection and conditions for popular abstrac...