We show that there is an O(n3) algorithm to approximate the bandwidth of an AT-free graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an O(e + n logn) algorithm to approximate the bandwidth of an AT-free graph within a factor 4 and anO(n+ e) algorithm with a factor 6. For the special cases of permutation graphs and trapezoid gr...

A classical result of De Bruijn and Erdős shows that any given n points are either collinear or determine at least n distinct lines in the plane. Chen and Chvátal conjectured that a generalization of this result in all metric spaces, with appropriate definitions of lines, holds as well. In this note, we show that the Chen-Chvátal generalization holds for Asteroidal-Triple free graphs, where lin...

To characterize the dynamical stability of an asteroid orbit, the calculation of its Lyapunov-Time TL is a widely used mean in celestial mechanics. In the present work we investigated the effects of the used computer hardware and integration method on the outcome of such stability computations. We showed that for some asteroids the change of the employed numerical method can change the obtained...

The Planck mission, originally devised for cosmological studies, offers the opportunity to observe Solar System objects at millimetric and submillimetric wavelengths. We concentrate in this paper on the asteroids of the Main Belt, a large class of minor bodies in the Solar System. At present more that 40000 of these asteroids have been discovered and their detection rate is rapidly increasing. ...

Introduction: Ca-Fe and alkali-halide alteration of CAIs is often attributed to aqueous alteration by fluids circulating on asteroidal parent bodies after the various chondritic components have been assembled, although debate continues about the roles of asteroidal vs. nebular modification processes [1-7]. Here we report detailed observations of alteration products in a large Type B2 CAI, TS4 f...

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...

We perform numerical simulations to study the secular orbital evolution and dynamical structure in the HD 69830 planetary system, using the best-fit orbital solutions by Lovis and coworkers. In the simulations, we show that a triplet Neptunian system is stable for at least 2 Gyr and that the stability would not be greatly influenced even if we varied the planetary masses. In addition, we employ...