Chordality of locally semicomplete and weakly quasi-transitive digraphs

Chordal graphs are important in the structural and algorithmic graph theory. A digraph analogue of chordal was introduced by Haskin Rose 1973 but has not been subject active studies until recently when a characterization semicomplete digraphs terms forbidden subdigraphs found Meister Telle. Locally digraphs, quasi-transitive extended amongst most popular generalizations digraphs. We extend subdigraph to locally introduce new class called weakly which contains symmetric is incomparable show that can be recursively constructed simple substitutions from transitive oriented graphs, This recursive construction similar one for demonstrates naturalness class. As by-product, we prove same The generalizes only recent results on also classical graphs.