Optimal lower bound on the number of variables for graph identification

Jin Yi Cai, Martin Furer, Neil Immerman

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    28 Scopus citations

    Abstract

    It is shown that Ω[n] variables are needed for first-order logic with counting to identify graphs on n vertices. This settles a long-standing open problem. The lower bound remains true over a set of graphs of color class size 4. This contrasts sharply with the fact that three variables suffice to identify all graphs of color class size 3, and two variables suffice to identify almost all graphs. The lower bound is optimal up to multiplication by a constant because n variables obviously suffice to identify graphs on n vertices.

    Original languageEnglish (US)
    Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
    PublisherPubl by IEEE
    Pages612-617
    Number of pages6
    ISBN (Print)0818619821, 9780818619823
    DOIs
    StatePublished - 1989
    Event30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA
    Duration: Oct 30 1989Nov 1 1989

    Publication series

    NameAnnual Symposium on Foundations of Computer Science (Proceedings)
    ISSN (Print)0272-5428

    Other

    Other30th Annual Symposium on Foundations of Computer Science
    CityResearch Triangle Park, NC, USA
    Period10/30/8911/1/89

    All Science Journal Classification (ASJC) codes

    • Hardware and Architecture

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