Algorithms, Combinatorics and Optimization Seminar
— 4:00pm
Location:
In Person
-
Wean Hall 8220
Speaker:
LUTZ WARNKE
,
Associate Professor, Department of Mathematics, University of California, San Diego
https://mathweb.ucsd.edu/people/profiles/lutz-warnke
Isomorphisms between dense random graphs.
Applied benchmark tests for the famous 'subgraph isomorphism problem' empirically discovered interesting phase transitions in random graphs. This motivates our rigorous study of two variants of the induced subgraph isomorphism problem for two independent binomial random graphs with constant edge-probabilities p1, p2. In particular, (i) we prove a sharp threshold result for the appearance of Gn,p1 as an induced subgraph of Gn,p2, (ii) we show two-point concentration of the size of the maximum common induced subgraph of Gn,p1 and Gn,p2, and (iii) we show that the number of induced copies of Gn,p1 in Gn,p2 has an unusual 'squashed lognormal' limiting distribution.
These results confirm simulation-based predictions of McCreesh, Prosser, Solnon and Trimble, and resolve several open problems of Chatterjee and Diaconis. The proofs are based on careful refinements of the first and second moment method, using extra twists to (a) take some non-standard behaviors into account, and (b) work around the large variance issues that prevent standard applications of the second moment method, using in particular pseudorandom properties and multi-round exposure arguments to tame the variance.
Based on joint work with Erlang Surya and Emily Zhu
Event Website:
https://aco.math.cmu.edu/abs-23-24/mar28.html