An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal graph is an interval graph if and only if it does not contain an asteroidal triple. In this paper, we...

Using the Bulirsh–Stoer method of integration, we investigated the migration of dust particles under the gravitational influence of all planets, radiation pressure, Poynting–Robertson drag and solar wind drag for equal to 0.01, 0.05, 0.1, 0.25, and 0.4. For silicate particles such values of correspond to diameters equal to about 40, 9, 4, 2, and 1 microns, respectively [1]. The relative error p...

Some meteorites are pieces of lava flows. They have the expected minerals present and the crystals are intertwined in a characteristic way indicative of crystallization in a lava flow. This shows that lavas erupted on at least some asteroids. Age dating indicates that the eruptions took place 4.5 billion years ago. Planetary scientists have recognized three main groups of asteroidal lava flows,...

We present O(n’R + n3R3) time algorithms to compute the treewidth, pathwidth, minimum fill-in and minimum interval graph completion of asteroidal triple-free graphs, where n is the number of vertices and R is the number of minimal separators of the input graph. This yields polynomial time algorithms for the four NP-complete graph problems on any subclass of the asteroidal triple-free graphs tha...

The conclusion of the classical ham sandwich theorem for bounded Borel sets may be strengthened, without additional hypotheses – there always exists a common bisecting hyperplane that touches each of the sets, that is, that intersects the closure of each set. In the discrete setting, where the sets are finite (and the measures are counting measures), there always exists a bisecting hyperplane t...