Cardinal invariants of closed graphs

TL;DR

This paper investigates the cardinal invariants of closed graphs on compact metrizable spaces, exploring their relationships and providing set-theoretic characterizations of analytic graphs with countable coloring numbers.

Contribution

It offers new insights into the cardinal characteristics of closed graphs and characterizes analytic graphs with countable coloring numbers using descriptive set theory.

Findings

Consistency results for bounding number and covering sets

Descriptive set theoretic characterization of analytic graphs with countable coloring number

Analysis of cardinal invariants in the context of closed graphs

Abstract

We study several cardinal characteristics of closed graphs G on compact metrizable spaces. In particular, we address the question when it is consistent for the bounding number to be strictly smaller than the smallest size of a set not covered by countably many compact G-anticliques. We also provide a descriptive set theoretic characterization of the class of analytic graphs with countable coloring number.