Cancelled due to COVID-19: Counting extensions revisited

Combinatorics Seminar
Friday, March 27, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Lutz Warnke – Georgia Tech –
Lutz Warnke

We consider rooted subgraphs in random graphs, i.e., extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three connecting two given vertices. 
In 1989, Joel Spencer gave sufficient conditions for the event that, with high probability, these extension counts are asymptotically equal for all choices of the root vertices.  
For the important strictly balanced case, Spencer also raised the fundamental question whether these conditions are necessary. 
We answer this question by a careful second moment argument, and discuss some intriguing problems that remain open.