• Corpus ID: 220713240

Infinite Stable Graphs With Large Chromatic Number

@article{Halevi2020InfiniteSG,
  title={Infinite Stable Graphs With Large Chromatic Number},
  author={Yatir Halevi and Itay Kaplan and Saharon Shelah},
  journal={arXiv: Logic},
  year={2020}
}

• Yatir Halevi, Itay Kaplan, S. Shelah
• Published 23 July 2020
• Mathematics
• arXiv: Logic

We prove that if $G=(V,E)$ is an $\omega$-stable (respectively, superstable) graph with $\chi(G)>\aleph_0$ (respectively, $2^{\aleph_0}$) then $G$ contains all the finite subgraphs of the shift graph $\text{Sh}_n(\omega)$ for some $n$. We prove a variant of this theorem for graphs interpretable in stationary stable theories. Furthermore, if $G$ is $\omega$-stable with $\mathrm{U}(G)\leq 2$ we prove that $n\leq 2$ suffices.