On the chromatic numbers of Johnson type graphs

Abstract

A Johnson type graph $J_{\pm}(n,k,t)$ is a graph whose vertex set consists of vectors from $\{-1,0,1\}^n$ of the length $\sqrt{k}$ and edges connect vertices with scalar product $t$. The paper determines the order of growth of the chromatic numbers of graphs $J_\pm(n,2,-1)$ and $J_\pm(n,3,-1)$ (logarithmic on $n$), and also $J_\pm(n,3,-2)$ (double logarithmic on $n$).