Abstract
Chordal graphs are important in structural 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 classes of locally semicomplete digraphs and weakly quasi-transitive digraphs.
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We are grateful to the anonymous referees for their careful reading and useful suggestions.
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Huang, J., Ye, Y.Y. Semi-strict Chordality of Digraphs. Graphs and Combinatorics 40, 56 (2024). https://doi.org/10.1007/s00373-024-02778-5
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DOI: https://doi.org/10.1007/s00373-024-02778-5