Email Gateway (Aug 19 2022 at 13:51): Email Gateway (Aug 19 2022 at 13:51):From: Tobias Nipkow <nipkow@in.tum.de>
Properties of Random Graphs -- Subgraph Containment
Lars Hupel
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.
http://afp.sourceforge.net/entries/Random_Graph_Subgraph_Threshold.shtml
Enjoy!
Last updated: Nov 21 2024 at 12:39 UTC