We present results of a project aimed at establishing a set of 12 spectro-photometric standards over a wide wavelength range from 320 to 2500 nm. Currently no such set of standard stars covering the near-IR is available. Our strategy is to extend the useful range of existing well-established optical flux standards (Oke 1990, Hamuy et al. 1992, 1994) into the near-IR by means of integral field spectroscopy with SINFONI at the VLT combined with state-of-the-art white dwarf stellar atmospheric models (TMAP, Holberg et al. 2008). As a solid reference, we use two primary HST standard white dwarfs GD71 and GD153 and one HST secondary standard BD+17 4708. The data were collected through an ESO “Observatory Programme” over ~40 nights between February 2007 and September 2008.

A graph G is threshold if there exists a ‘weight’ function w: V(G) → R such that the total weight of any stable set of G is less than the total weight of any non-stable set of G. Let n denote the set of threshold graphs with n vertices. A graph is called n-universal if it contains every threshold graph with n vertices as an induced subgraph. n-universal threshold graphs are of special interest, since they are precisely those n-universal graphs that do not contain any non-threshold induced subgraph.

In this paper we shall study minimumn-universal (threshold) graphs, i.e.n-universal (threshold) graphs having the minimum number of vertices.

It is shown that for any n ≥ 3 there exist minimum n-universal graphs, which are themselves threshold, and others which are not.

Two extremal minimum n-universal graphs having respectively the minimum and the maximum number of edges are described, it is proved that they are unique, and that they are threshold graphs.

The set of all minimum n-universal threshold graphs is then described constructively; it is shown that it forms a lattice isomorphic to the n − 1 dimensional Boolean cube, and that the minimum and the maximum elements of this lattice are the two extremal graphs introduced above.

The proofs provide a (polynomial) recursive procedure that determines for any threshold graph G with n vertices and for any minimum n-universal threshold graph T, an induced subgraph G' of T isomorphic to G.

The Sun’s activity has been evolving in the ascending phase of Solar Cycle 23 since 1996. Similarly, the research on solar activity is also in the ascending phase of a new active period. Numerous new results have been obtained from a large amount of space and ground observations covering a wide spectral range. In particular, observations with YOHKOH, SOHO, and TRACE have revealed a multitude of phenomena and processes in the solar atmosphere which provide us a new picture of the Sun.