Random induced graphs
Given a monotone graphical property Q, how large should d(n) be to ensure that if (Hn) is any sequence of graphs satisfying |Hn| = n and δ(Hn) ≥ d(n), then almost every induced subgraph of Hn has property Q? We prove essentially best possible results for the following monotone properties: (i) k-connected for fixed k, (ii) Hamiltonian. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Random induced graphs; Monotone properties PII: S0012-365X(01)00345-4.
Bollobäs, B., Erdös, P., Faudree, R., Rousseau, C., & Schelp, R. (2002). Random induced graphs. Discrete Mathematics, 248 (1-3), 249-254. https://doi.org/10.1016/S0012-365X(01)00345-4