Quentin Dubroff, Rutgers University

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.

See: https://sites.google.com/view/rutgersdmseminar