Semi-strict chordality of digraphs

TL;DR

This paper introduces semi-strict chordal digraphs, a new class between chordal digraphs and graphs, with rich structural properties and characterizations, advancing understanding of digraph chordality.

Contribution

It defines semi-strict chordal digraphs, characterizes them via knotting graphs, and provides forbidden subdigraph characterizations in specific digraph classes.

Findings

Semi-strict chordal digraphs form a new class with structural properties.

Characterization via knotting graphs links to Gallai's comparability graphs.

Forbidden subdigraphs identified for certain digraph classes.

Abstract

Chordal graphs are important in algorithmic graph theory. Chordal digraphs are a digraph analogue of chordal graphs and have been a subject of active studies recently. Unlike chordal graphs, chordal digraphs lack many structural properties such as forbidden subdigraph or representation characterizations. In this paper we introduce the notion of semi-strict chordal digraphs which form a class strictly between chordal digraphs and chordal graphs. Semi-strict chordal digraphs have rich structural properties. We characterize semi-strict chordal digraphs in terms of knotting graphs, a notion analogous to the one introduced by Gallai for the study of comparability graphs. We also give forbidden subdigraph characterizations of semi-strict chordal digraphs within the cases of locally semicomplete digraphs and weakly quasi-transitive digraphs.