Thresholds in random motif graphs

Michael Anastos, Peleg Michaeli, Samantha Petti

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    We introduce a natural generalization of the Erdős-Rényi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph G(H, n, p) is the random (multi)graph obtained by adding an instance of a fixed graph H on each of the copies of H in the complete graph on n vertices, independently with probability p. We establish that every monotone property has a threshold in this model, and determine the thresholds for connectivity, Hamiltonicity, the existence of a perfect matching, and subgraph appearance. Moreover, in the first three cases we give the analogous hitting time results; with high probability, the first graph in the random motif graph process that has minimum degree one (or two) is connected and contains a perfect matching (or Hamiltonian respectively).

    Original languageEnglish
    Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
    EditorsDimitris Achlioptas, Laszlo A. Vegh
    PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
    ISBN (Electronic)9783959771252
    DOIs
    StatePublished - Sep 2019
    Event22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019 - Cambridge, United States
    Duration: 20 Sep 201922 Sep 2019

    Publication series

    NameLeibniz International Proceedings in Informatics, LIPIcs
    Volume145
    ISSN (Print)1868-8969

    Conference

    Conference22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
    Country/TerritoryUnited States
    CityCambridge
    Period20/09/1922/09/19

    Keywords

    • Connectivity
    • Hamiltonicty
    • Random graph
    • Small subgraphs

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