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  • Characterizing and decomposing classes of threshold, split, and bipartite graphs via 1-Sperner hypergraphs [Elektronski vir]
    Boros, Endre ; Gurvich, Vladimir ; Milanič, Martin, 1980-
    A hypergraph is said to be 1-Sperner if for every twohyperedges the smallest of their two set differences is of size one. We present several applications of 1-Spernerhypergraphs to graphs. First, we ... consider several waysof associating hypergraphs to graphs, namely, vertex cover, clique, independent set, dominating set, and closed neighborhood hypergraphs. For each of them, wecharacterize graphs yielding 1-Sperner hypergraphs.These results give new characterizations of threshold and domishold graphs. Second, we apply a characteriza-tion of 1-Sperner hypergraphs to derive decomposition theorems for two classes of split graphs, a class of bipartite graphs, and a class of cobipartite graphs. These decomposition theorems, based on certain matrix partitions, lead to new classes of graphs of bounded clique-width and new polynomially solvable cases of three basic domination problems: domination, totaldomination, and connected domination.
    Vir: Journal of graph theory [Elektronski vir]. - ISSN 1097-0118 (Vol. 94, no. 3, 2020, str. 364-397)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2020
    Jezik - angleški
    COBISS.SI-ID - 1541798340

    Povezava(-e):

    https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.22529
    DOI

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