@article{486712b377ed4f96a577186fc192d3ec,

title = "INFINITE STABLE GRAPHS WITH LARGE CHROMATIC NUMBER",

abstract = "We prove that if G = (V, E) is an ω-stable (respectively, superstable) graph with χ(G) > ℵ0 (respectively, 2ℵ0 ) then G contains all the finite subgraphs of the shift graph Shn(ω) for some n. We prove a variant of this theorem for graphs interpretable in stationary stable theories. Furthermore, if G is ω-stable with U(G) ≤ 2 we prove that n ≤ 2 suffices.",

keywords = "Chromatic number, Stable graphs, Taylor{\textquoteright}s conjecture",

author = "Yatir Halevi and Itay Kaplan and Saharon Shelah",

note = "Funding Information: Received by the editors August 4, 2020, and, in revised form, September 13, 2020, and July 21, 2021. 2020 Mathematics Subject Classification. Primary 03C45; Secondary 05C15. Key words and phrases. Chromatic number, stable graphs, Taylor{\textquoteright}s conjecture. For the first author, this research was supported by the Israel Science Foundation (grant No. 181/16) and the Kreitman foundation fellowship. For the second author, this research (grants no. 1533/14 and 1254/18) was supported by the Israel Science Foundation. The third author was supported by the Israel Science Foundation grant no: 1838/19 and the European Research Council grant 338821. Paper no. 1196 in the third author{\textquoteright}s publication list. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society.",

year = "2022",

month = jan,

day = "1",

doi = "10.1090/tran/8570",

language = "English",

volume = "375",

pages = "1767--1799",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "3",

}