Seminar Details
On the H-space of a Random Graph
- Start Date: November 20, 2023
- Event Start Time: 2:00 PM
- Event End Time: 3:00 PM
- Seminar Series: Rutgers Discrete Mathematics Seminar
- Presenter(s): Quentin Dubroff - Rutgers University
- Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
- Event Additional Info: <p>See: <a href="https://sites.google.com/view/rutgersdmseminar">https://sites.google.com/view/rutgersdmseminar</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
The edge space of a graph G is the vector space of functions from E(G) to F_2 (the two-element field) with members naturally identified with subgraphs of G, and the H-space is the subspace spanned by copies of the graph H. We are interested in understanding when the random graph is likely to have the most generic possible H-space. For example, if H is a triangle, we want to know when it is likely that every cycle is in the H-space (i.e. when the triangle space is likely the same as the cycle space). We give an essentially complete answer for strictly 2-balanced graphs, showing that a simple necessary condition in fact characterizes when the H-space is as generic as possible.
Joint with Jeff Kahn.