Geodesic
Chromatic Numbers of Some Distance Graphs
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 210-220

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For positive integers $n>r>s$, $G(n,r,s)$ is the graph whose vertices are the $r$-element subsets of an $n$-element set, two subsets being adjacent if their intersection contains exactly $s$ elements. We study the chromatic numbers of this family of graphs. In particular, the exact value of the chromatic number of $G(n,3,2)$ is found for infinitely many $n$. We also improve the best known upper bounds for chromatic numbers for many values of the parameters $r$ and $s$ and for all sufficiently large $n$.
Keywords: chromatic number, distance graph, upper bound. 
@article{MZM_2020_107_2_a3,
     author = {D. A. Zakharov},
     title = {Chromatic {Numbers} of {Some} {Distance} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {210--220},
     publisher = {mathdoc},
     volume = {107},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a3/}
}
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D. A. Zakharov. Chromatic Numbers of Some Distance Graphs. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 210-220. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a3/