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  • Conformality of minimal transversals of maximal cliques
    Boros, Endre ...
    Given a hypergraph ℋ, the dual hypergraph of ℋis the hypergraph of all minimal transversals of ℋ. A hypergraph is conformal if it is the family of maximal cliques of a graph. In a recent work, Boros, ... Gurvich, Milanič, and Uno (Journal of Graph Theory, 2025) studied conformality of dual hypergraphs and proved several results related to this property, leading in particular to a polynomial-time algorithm for recognizing graphs in which, for any fixed k, all minimal transversals of maximal cliques have size at most k. In this follow-up work, we provide a novel aspect to the study of graph clique transversals, by considering the dual conformality property from the perspective of graphs. More precisely, we study graphs for which the family of minimal transversals of maximal cliques is conformal. Such graphs are called clique dually conformal (CDC for short). It turns out that the class of CDC graphs is a rich generalization of the class of P4-free graphs. As our main results, we completely completely characterize CDC graphs within the families of triangle-free graphs and split graphs. Both characterizations lead to polynomial-time recognition algorithms. Generalizing the fact that every P4-free graph is CDC, we also show that the class of CDC graphs is closed under substitution, in the strong sense that substituting a graph H for a vertex of a graph G results in a CDC graph if and only if both G and H are CDC.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 349, iss. 1, [article no.] 114657, Jan. 2026, str. 1-25)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2026
    Jezik - angleški
    COBISS.SI-ID - 261722883

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0012365X25002651?via%3Dihub
    Repozitorij Univerze na Primorskem - RUP
    DOI

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 349, iss. 1, [article no.] 114657, Jan. 2026, str. 1-25)
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