Geodesic
On the chromatic numbers of Johnson-type graphs
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 192-200 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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},
     year = {2022},
     volume = {518},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a6/}
}
TY  - JOUR
AU  - D. D. Cherkashin
TI  - On the chromatic numbers of Johnson-type graphs
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 192
EP  - 200
VL  - 518
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a6/
LA  - ru
ID  - ZNSL_2022_518_a6
ER  - 
%0 Journal Article
%A D. D. Cherkashin
%T On the chromatic numbers of Johnson-type graphs
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 192-200
%V 518
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a6/
%G ru
%F 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/

[1] D. Cherkashin and S. Kiselev, Independence numbers of Johnson-type graphs, 2019, arXiv: 1907.06752

[2] P. Frankl and A. Kupavskii, “Intersection theorems for $\{0,\pm 1\ $-vectors and $s$-cross-intersecting families”, Moscow Journal of Combinatorics and Number Theory, 2:7 (2017), 91–109

[3] P. Frankl and A. Kupavskii, “Correction to the Intersection theorems for $\{0,\pm 1\ $-vectors and $s$-cross-intersecting families”, Moscow Journal of Combinatorics and Number Theory, 8:4 (2019), 389–391

[4] L. Lovász, “On the ratio of optimal integral and fractional covers”, Discrete mathematics, 13:4 (1975), 383–390