We present a polynomial time algorithm to compute a minimum (weight) feedback vertex set for AT-free graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.

We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triple-free graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating set on a large superclass of the asteroidal triple-free graphs, called DDP-graphs. These algorithms...

We introduce a special decomposition, the so-called split-minors, of the reduced clique graphs of chordal graphs. Using this notion, we characterize asteroidal sets in chordal graphs and clique trees with minimum number of leaves.

An asteroidal triple in a graph is a set of three non-adjacent vertices such that for any two of them there exists a path between them that does not intersect the neighborhood of the third. An asteroidal quadruple is a set of four non-adjacent vertices such that any three of them is an asteroidal triple. In this paper, we study a subclass of directed path graph, the class of extended star direc...

An asteroidal triple is a set of three independent vertices in a graph such that any two vertices in the set are connected by a path which avoids the neighbourhood of the third. A classical result by Lekkerkerker and Boland [10] showed that interval graphs are precisely the chordal graphs that do not have asteroidal triples. Interval graphs are chordal, as are the directed path graphs and the p...

Circle graphs are intersection graphs of chords in a circle and kpolygon graphs are the intersection graphs of chords in a convex ksided polygon where each chord has its endpoints on distinct sides. Every k-polygon graph is a circle graph and every circle graph is a kpolygon graph for some k. The polygon number ψ(G) of a circle graph G is the minimum k such that G is a k-polygon graph and the p...

We settle two conjectures on domination-search, a game proposed by Fomin et.al. [1], one in affirmative and the other in negative. The two results presented here are (1) domination search number can be greater than domination-target number, (2) domination search number for asteroidal-triple-free graphs is at most 2.

An asteroidal triple in a graph G is a set of three nonadjacent vertices such that for any two of them there exists a path between them that does not intersect the neighborhood of the third. Special asteroidal triple in a graph G is an asteroidal triple such that each pair is linked by a special connection. A special asteroidal triples play a central role in a characterization of directed path ...

We numerically investigate the migration of dust particles with initial orbits close to those of the numbered asteroids, observed trans-Neptunian objects, and comet Encke. The fraction of silicate asteroidal particles that collided with the Earth during their lifetime varied from 11% for 100 micron particles to 0.008% for 1 micron particles. Almost all asteroidal particles with diameter d >/= 4...