2025/09/23 by Pavol Hell, Hell, Pavol, César Hernández‐Cruz +3
Computer Science · Mathematics · #05C20 #05C75 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2509.18541
openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency matrix does not contain the Γ matrix as a submatrix. In general, it is not clear if these digraphs can be recognized in polynomial time. We focus on multipartite tournaments with possible loops. We give a polynomial-time recognition algorithm and a forbidden induced subgraph characterization of the strong chordality for each of the following cases: tournaments with possible loops, reflexive multipartite tournaments, irreflexive bipartite tournaments, irreflexive tournaments minus one arc, and balanced digraphs. In addition, we prove that in a strongly chordal digraph the minimum size of a total dominating set equals the maximum number of disjoint in-neighborhoods, and this number can be calculated in linear time given a Γ-free ordering of the input graph.