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 $n$).

Published in Russian in Zapiski Nauchnykh Seminarov POMI. This translation will appear in Journal of Mathematical Sciences