Properties of Random Graphs -- Subgraph Containment

Lars Hupel 🌐

February 13, 2014

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


Random graphs are graphs with a fixed number of vertices, where each edge is present with a fixed probability. We are interested in the probability that a random graph contains a certain pattern, for example a cycle or a clique. A very high edge probability gives rise to perhaps too many edges (which degrades performance for many algorithms), whereas a low edge probability might result in a disconnected graph. We prove a theorem about a threshold probability such that a higher edge probability will asymptotically almost surely produce a random graph with the desired subgraph.


BSD License


Session Random_Graph_Subgraph_Threshold