Trees, ladders and graphs
D\'aniel T. Soukup

TL;DR
This paper presents a novel method for constructing uncountably chromatic graphs using non special trees and ladder systems, answering longstanding questions about graph connectivity and subgraph structures.
Contribution
It introduces a new construction technique for uncountably chromatic graphs and addresses open problems related to connectivity and subgraph configurations.
Findings
Constructed graphs of chromatic number ω₁ without uncountable ω-connected subgraphs.
Built triangle-free graphs of chromatic number ω₁ lacking specific subgraphs.
Provided answers to questions posed by Erdős and Hajnal in 1985.
Abstract
We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erd\H{o}s and A. Hajnal from 1985, we construct graphs of chromatic number without uncountable -connected subgraphs. Second, we build triangle free graphs of chromatic number without subgraphs isomorphic to .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Computability, Logic, AI Algorithms
