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...

The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n − lg n− 1 2 lg lg n+O(1). The proper leafage l(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and...

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,...

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. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-dis...

An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the AT-free graphs provide a common generalization of interval, permutation, trapezoid...

Since its introduction to recognize chordal graphs by Rose, Tarjan, and Lueker, Lexicographic Breadth First Search (LexBFS) has been used to come up with simple, often linear time, algorithms on various classes of graphs. These algorithms, called multi-sweep algorithms, compute a number of LexBFS orderings σ1, . . . , σk, where σi is used to break ties for σi+1, we write LexBFS (σi) = σi+1. For...