Year: 2026
Type: preprint
Abstract: The study of three-vertex subgraph densities has developed along two complementary lines: exact finite realization in large graphs of a given order, and asymptotic approximate realization by sequences of graphs. We bridge these viewpoints for the edge density and the four induced three-vertex subgraph densities. By analyzing local modifications of finite samples from graphons, we show that, for any nonempty subset of these densities, every asymptotically feasible target vector lying a fixed positive distance from the boundary of the corresponding feasible region is realized exactly by a graph of every sufficiently large order, subject only to the natural arithmetic constraints. Thus, in the interior of these feasible regions, asymptotic feasibility implies exact finite realizability up to the unavoidable arithmetic obstructions.
Source: arXiv (Cornell University)
Author: Schein, Hillel
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223396016