Birth of a giant \((k_{1},k_{2})\)-core in the random digraph

DOI10.1016/j.aam.2017.01.006zbMath1358.05126arXiv1608.05095OpenAlexW2964313783MaRDI QIDQ515812

Boris G. Pittel, Daniel J. Poole

Publication date: 16 March 2017

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.05095

zbMATH Keywords

threshold number of edges

Mathematics Subject Classification ID

Trees (05C05) Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05) Directed graphs (digraphs), tournaments (05C20) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (2)

\(H\)-sequences and 2-step coreness in graphs ⋮ Counting directed acyclic and elementary digraphs

Cites Work

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• Asymptotic normality of the \(k\)-core in random graphs
• Size and connectivity of the \(k\)-core of a random graph
• Counting connected graphs inside-out
• Sudden emergence of a giant \(k\)-core in a random graph
• Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs
• Counting strongly-connected, moderately sparse directed graphs
• Asymptotic enumeration of strongly connected digraphs by vertices and edges
• The critical behavior of random digraphs
• The transitive closure of a random digraph
• Almost all graphs with 1.44n edges are 3-colorable
• The phase transition in the evolution of random digraphs
• Counting strongly connected (k₁, k₂)‐directed cores
• Cores in random hypergraphs and Boolean formulas
• Thek-Core and Branching Processes

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