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arXiv · 1603.05134

The chromatic number of finite type-graphs

Christian Avart·Bill Kay·Christian Reiher·Vojtěch Rödl
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Abstract

By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]=\{1,2,\ldots, n\}$ for some integers $n\ge k\ge 1$, and in which two such sets are adjacent if and only if they realise a certain order type specified in advance. Examples of such graphs have been investigated in a great variety of contexts in the literature with particular attention being paid to their chromatic number. In recent joint work with Tomasz {\L}uczak, two of the authors embarked on a systematic study of the chromatic numbers of such type-graphs, formulated a general conjecture determining this number up to a multiplicative factor, and proved various results of this kind. In this article we fully prove this conjecture.

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Christian Avart, Bill Kay, Christian Reiher, Vojtěch Rödl. 2016-03-16. The chromatic number of finite type-graphs. https://doi.org/10.1016/j.jctb.2016.10.004

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