INDIAN STATISTICAL INSTITUTE

(Headquarters at Kolkata)

203 B. To Road, Kolkata 700 108

Random Graphs

Optional Course for B. Stat. IIIrd Year

Academic Year 2019 - 2020: Semester II

Project S4

• Title: Sub-Graph Containment Threshold for the Erdős-Rényi Binomial Random Graphs

• Goal: The main objective of the project is to determine that containment of a specific fix sub-graph has a threshold and to demonstrate a specific threshold. It is also to be shown that for certain sub-graphs the threshold need not be a sharp threshold. Is it possible that for certain sub-graphs it is indeed a sharp threshold?

• Remarks: This is essentially a reading project. A lot of materials can be found in the Chapter 3 of S. Janson, T. Łuczak and A. Riciński: Random Graphs book and other references therein.