Open AccessIsolated cycles of critical random graphs
Author(s) -
Marc Noy,
Vonjy Rasendrahasina,
Vlady Ravelomanana,
Juanjo Rué
Publication year - 2017
Language(s) - English
Resource type - Conference proceedings
DOI - 10.1137/1.9781611974775.4
Subject(s) - combinatorics , mathematics , random graph , discrete mathematics , random regular graph , set (abstract data type) , graph , graph theory , computer science , pathwidth , line graph , programming language
Consider the Erdős-Rényi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of ( n 2 ) edges. Let L be a set of positive integers. For any number of edges M 6 n 2 +o(n), we compute – via analytic combinatorics – the number of isolated cycles of G(n, M) whose length is in L.
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