Trees, ladders and graphs

Abstract

We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erdős and A. Hajnal from 1985, we construct graphs of chromatic number ${\omega }_1$ without uncountable $\omega$-connected subgraphs. Second, we build triangle free graphs of chromatic number ${\omega }_1$ without subgraphs isomorphic to $H_{\omega ,\omega +2}$.

23 pages, 2 figures, submitted to the Journal of Comb. Theory Series B

Cited by in corpus (1)

• Davies-trees in infinite combinatorics