Thek-Core and Branching Processes

DOI10.1017/S0963548307008589zbMath1136.05071arXivmath/0511093MaRDI QIDQ5448993

Oliver Riordan

Publication date: 10 March 2008

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511093

zbMATH Keywords

power-lawscale-free graphGalton-Watson branching processRandom graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Random graphs (graph-theoretic aspects) (05C80) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Vertex degrees (05C07)

Related Items (19)

Continuous phase transitions on Galton–Watson trees ⋮ How does the core sit inside the mantle? ⋮ The structure of typical clusters in large sparse random configurations ⋮ Singularity of the \(k\)-core of a random graph ⋮ Propagation of chaos of forward-backward stochastic differential equations with graphon interactions ⋮ A central limit theorem for diffusion in sparse random graphs ⋮ Random Simplicial Complexes: Around the Phase Transition ⋮ Phase transitions in graphs on orientable surfaces ⋮ The cook-book approach to the differential equation method ⋮ Birth of a giant \((k_{1},k_{2})\)-core in the random digraph ⋮ The Stripping Process Can be Slow: Part II ⋮ Random graphs with forbidden vertex degrees ⋮ Survival probabilities for \(N\)-ary subtrees on a Galton-Watson family tree ⋮ On the robustness of random \(k\)-cores ⋮ Core forging and local limit theorems for the \(k\)-core of random graphs ⋮ Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT ⋮ Loose cores and cycles in random hypergraphs ⋮ An old approach to the giant component problem ⋮ Cores of random graphs are born Hamiltonian

Cites Work

• Sudden emergence of a giant \(k\)-core in a random graph
• A Random Graph Model for Power Law Graphs
• Emergence of Scaling in Random Networks
• A simple solution to the k‐core problem
• The phase transition in the uniformly grown random graph has infinite order
• The phase transition in inhomogeneous random graphs
• Cores in random hypergraphs and Boolean formulas
• Families of Non-disjoint subsets
• The Small Giant Component in Scale-Free Random Graphs

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