The chromatic number of finite type-graphs

https://doi.org/10.1016/j.jctb.2016.10.004Get rights and content
Under an Elsevier user license
open archive

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,,n} for some integers nk1, 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 Łuczak, 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.

Keywords

Shift graphs
Type-graphs
Chromatic number
Order types of pairs

Cited by (0)

1

The second author was supported by NCN grant 2012/06/A/STI/00261 and by NSF grant DMS 1301698.

2

The fourth author was supported by NSF grants DMS 1301698 and 1102086.