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Different capacities of a digraph

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Abstract

Sperner product is the natural generalization of co-normal product to digraphs. For every class of digraphs closed under Sperner product, the cardinality of the largest subgraph from the given class, contained as an induced subgraph in the co-normal powers of a graphG, has an exponential growth. The corresponding asymptotic exponent is the capacity ofG with respect to said class of digraphs. We derive upper and lower bounds for these capacities for various classes of digraphs, and analyze the conditions under which they are tight.

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Authors and Affiliations

  1. IASI-CNR, viale Manzoni 30, 00185, Roma, Italy

    Anna Galluccio

  2. Dipartimento di Informatica, Università di Salerno, 84081, Baronissi, SA, Italy

    Luisa Gargano

  3. Dipartimento di Scienze dell’Informazione, Università “La Sapienza”, via Salaria 113, 00198, Roma, Italy

    János Körner

  4. Mathematical Institute of HAS, POB127, 1364, Budapest, Hungary

    Gábor Simonyi

Authors
  1. Anna Galluccio
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  2. Luisa Gargano
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  3. János Körner
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  4. Gábor Simonyi
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Additional information

During different parts of this research this author enjoyed hospitality and support of IASI-CNR, Roma and SFB 343, Universität Bielefeld.

During different parts of this research this author enjoyed hospitality and support of IASI-CNR, Roma and DIMACS Center, Rutgers University.

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Galluccio, A., Gargano, L., Körner, J. et al. Different capacities of a digraph. Graphs and Combinatorics 10, 105–121 (1994). https://doi.org/10.1007/BF02986655

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  • DOI: https://doi.org/10.1007/BF02986655

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