An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triple-free (AT-free, for short) if it contains no asteroidal triple. The motivation for this work is provided, in part, by the fact that AT-free graphs ooer a common generalization of interval, permutation...

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

I INTRODUCTION The existence of regoliths on asteroidal surfaces is supported by recent telescopic observations. On the other hand the constituent grains of gas-rich meteorites have been clearly irradiated as individual grains in both the ancient solar wind (SW) and solar cosmic rays (SCR). This irradiation could have occured within an asteroidal regolith, before the compaction of the grains in...

We investigate the properties of chordal graphs that follow from the well-known fact that chordal graphs admit tree representations. In particular, we study the structure of reduced clique graphs which are graphs that canonically capture all tree representations of chordal graphs. We propose a novel decomposition of reduced clique graphs based on two operations: edge contraction and removal of ...