Work

Classification of countable 2-colored ultrahomogeneous graphs where each color class forms a disjoint union of cliques

Year: 2024

Type: article

Abstract: We classify the countable ultrahomogeneous 2-vertex-colored graphs in which the color classes form disjoint unions of cliques. This generalizes work by Jenkinson et. al. (2012), Lockett and Truss (2014) as well as Rose (2011) on ultrahomogeneous n -graphs. As the key aspect in such a classification, we identify a concept called piecewise ultrahomogeneity. We prove that there are two specific graphs whose occurrence essentially dictates whether a graph is piecewise ultrahomogeneous, and we exploit this fact to prove the classification.

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2024.104093

Authors: Sofia Brenner, Irene Heinrich

Institution: Technische Universität Darmstadt

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,000

Funders: Deutsche Forschungsgemeinschaft, European Research Council, Horizon 2020, H2020 European Research Council