Threshold functions for small subgraphs: an analytic approach [article]

Gwendal Collet, Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger, Vlady Ravelomanana
<span title="2017-05-24">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the possible overlapping of copies. This paper is a version, extended to include proofs, of the paper with the same title to be presented at the Eurocomb 2017 meeting.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:1705.08768v1</a> <a target="_blank" rel="external noopener" href="">fatcat:wwwwa4zy5zer7jvfuj46ah44p4</a> </span>
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