On the chromatic numbers of Johnson-type graphs
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 192-200
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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 $n$).
@article{ZNSL_2022_518_a6,
author = {D. D. Cherkashin},
title = {On the chromatic numbers of {Johnson-type} graphs},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {192--200},
publisher = {mathdoc},
volume = {518},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a6/}
}
D. D. Cherkashin. On the chromatic numbers of Johnson-type graphs. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 192-200. http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a6/