An \emph{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 \cite{6} showed that interval graphs are precisely the chordal graphs that do not have asteroidal triples.
Interval graphs are chordal, as are the \emph{directed path graphs} and the \emph{path graphs}.
Similar to Lekkerkerker and Boland, Cameron, Ho\'{a}ng, and L… CONTINUE READING