Algebraic Properties of a Hypergraph Lifting Map
Mark Budden, Josh Hiller, Tommy Meek, and Andrew Penland
TL;DR
This paper interprets a hypergraph lifting map as a linear transformation, enabling algebraic analysis that yields new lower bounds for specific 3-uniform hypergraph Ramsey numbers.
Contribution
It introduces an algebraic perspective on the hypergraph lifting map, providing new structural insights and bounds in hypergraph Ramsey theory.
Findings
Lifting map can be viewed as a linear transformation
Algebraic techniques reveal structural properties of the lifting map
New lower bounds for certain 3-uniform hypergraph Ramsey numbers
Abstract
Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain -uniform hypergraph to a given graph, bounding cliques in a predictable way. In this paper, we interpret the lifting map as a linear transformation. This interpretation allows us to use algebraic techniques to prove several structural properties of the lifting map, culminating in new lower bounds for certain -uniform hypergraph Ramsey numbers.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Advanced Graph Theory Research