# 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} }

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.

## 2 Citations

Infinite Stable Graphs With Large Chromatic Number II

- Mathematics
- 2021

We prove a version of the strong Taylor’s conjecture for stable graphs: if G is a stable graph whose chromatic number is strictly greater than i2(א0) then G contains all finite subgraphs of Shn(ω)…

LIST OF PUBLICATIONS

- Environmental Science
- 2022

1. Sh:a Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-New…

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