Genericity of chaos for colored graphs

TL;DR

This paper extends the concept of chaos to colored graphs by associating them with a universal space and proves that chaotic and almost chaotic colored graphs are topologically generic within this space.

Contribution

It introduces a new framework for analyzing chaos in colored graphs and establishes the genericity of chaotic behavior in this setting.

Findings

Chaotic colored graphs are topologically generic.

Almost chaotic colored graphs are also topologically generic.

The framework generalizes chaos concepts to graph structures.

Abstract

To each colored graph, one can associate its closure in the universal space of isomorphism classes of pointed colored graphs, and this subspace can be regarded as a generalized subshift. Based on this correspondence, we extend the notion of chaotic dynamical systems to colored graphs. We introduce definitions for chaotic and almost chaotic (colored) graphs, and prove their topological genericity in various subsets of the universal space.