Homomorphism densities of graphs in kernels
Date
2025
Authors
Turton, Chris
Journal Title
Journal ISSN
Volume Title
Publisher
University Of Victoria
Abstract
This project explores the branch of Mathematics known as graph theory, where a graph is a set of vertices paired with a set of edges. We define an abstraction of a graph known as a kernel, and we explore various problems about the homomorphism density of a graph in a kernel.
In particular, we generalize previous results about decomposing sums of densities of odd cycles in terms of the simpler densities of paths. In addition, we investigate lower bounds for inequalities involving certain density sums. We provide several explicit kernel constructions which certify that some of these bounds are sharp.
Description
Keywords
mathematics, graph, graph theory, kernel, graphon, homomorphism density