Lattice exit models

TL;DR

Lattice exit models are a class of problems involving graph labeling that serve as educational exercises and also illustrate complex independence results in set theory, with implications in combinatorics and algorithms.

Contribution

This paper introduces lattice exit models as a framework connecting graph labeling exercises with large-scale regularities and set-theoretic independence results.

Findings

Provides geometric examples of ZFC independence.

Discusses combinatorial implications of lattice exit models.

Highlights algorithmic considerations for labeling problems.

Abstract

We discuss a class of problems which we call lattice exit models. At one level, these problems provide undergraduate level exercises in labeling the vertices of graphs (e.g., depth first search). At another level (theorems about large scale regularities of labels) they provide concrete geometric examples of ZFC independence. We note some combinatorial and algorithmic implications.