Asymptotics of the independence number of a random subgraph of the graph $G(n,r,{}s)$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 205 (2022), pp. 16-21.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we discuss the probabilistic version of the classical problem of extremal combinatorics stated appeared in the middle of the 20th century by P. Erdős, C. Ko, and R. Rado.
Keywords: random graph, extremal system of sets, hypergraph.
@article{INTO_2022_205_a2,
     author = {A. M. Raigorodskii},
     title = {Asymptotics of the independence number of a random subgraph of the graph $G(n,r,{<}s)$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {16--21},
     publisher = {mathdoc},
     volume = {205},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_205_a2/}
}
TY  - JOUR
AU  - A. M. Raigorodskii
TI  - Asymptotics of the independence number of a random subgraph of the graph $G(n,r,{<}s)$
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 16
EP  - 21
VL  - 205
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_205_a2/
LA  - ru
ID  - INTO_2022_205_a2
ER  - 
%0 Journal Article
%A A. M. Raigorodskii
%T Asymptotics of the independence number of a random subgraph of the graph $G(n,r,{<}s)$
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 16-21
%V 205
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_205_a2/
%G ru
%F INTO_2022_205_a2
A. M. Raigorodskii. Asymptotics of the independence number of a random subgraph of the graph $G(n,r,{<}s)$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 205 (2022), pp. 16-21. http://geodesic.mathdoc.fr/item/INTO_2022_205_a2/

[1] Bobu A. V., Kupriyanov A. E., Raigorodskii A. M., “Ob odnom obobschenii knezerovskikh grafov”, Mat. zametki., 107:3 (2020), 351–365 | MR | Zbl

[2] Ipatov M. M., Koshelev M. M., Raigorodskii A. M., “Modulyarnost nekotorykh distantsionnykh grafov”, Dokl. RAN., 490 (2020), 71–73 | Zbl

[3] Pushnyakov F. A., Raigorodskii A. M., “Otsenka chisla reber v osobykh podgrafakh nekotorogo distantsionnogo grafa”, Mat. zametki., 107:2 (2020), 286–298 | MR | Zbl

[4] Pushnyakov F. A., Raigorodskii A. M., “Otsenka chisla reber v podgrafakh grafov Dzhonsona”, Dokl. RAN., 499:1 (2021), 40–43 | Zbl

[5] Pyaderkin M. M., “Ob ustoichivosti v teoreme Erdesha—Ko—Rado”, Dokl. RAN., 462:2 (2015), 144–147 | MR | Zbl

[6] Pyaderkin M. M., “O porogovoi veroyatnosti dlya ustoichivosti nezavisimykh mnozhestv v distantsionnom grafe”, Mat. zametki., 106:2 (2019), 280–294 | MR | Zbl

[7] Raigorodskii A. M., Koshelev M. M., “Novye otsenki kliko-khromaticheskikh chisel grafov Dzhonsona”, Dokl. RAN., 490 (2020)), 78–80 | Zbl

[8] Raigorodskii A. M., Cherkashin D. D., “Ekstremalnye zadachi v raskraskakh gipergrafov”, Usp. mat. nauk., 2020, no. 1, 95–154 | Zbl

[9] Raigorodskii A. M., Shishunov E. D., “O chislakh nezavisimosti nekotorykh distantsionnykh grafov s vershinami v $\{-1,0,1\}^n$”, Dokl. RAN., 485:3 (2019), 269–271 | Zbl

[10] Raigorodskii A. M., Shishunov E. D., “O chislakh nezavisimosti distantsionnykh grafov s vershinami v $\{-1,0,1\}^n$”, Dokl. RAN., 488:5 (2019), 486–487 | Zbl

[11] Balogh J., Cherkashin D., Kiselev S., “Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs”, Eur. J. Combin., 79 (2019), 228–236 | DOI | MR | Zbl

[12] Erdős P., Ko C., Rado R., “Intersection theorems for systems of finite sets”, Quart. J. Math., 12:1 (1961), 313–-320 | DOI | MR | Zbl

[13] Frankl P., “On intersecting families of finite sets”, J. Combin. Theory Ser. A, 24 (1978), 146–161 | DOI | MR | Zbl

[14] Kiselev S., Kupavskii A., Sharp bounds for the chromatic number of random Kneser graphs, arXiv: 1810.01161 [math.CO] | MR

[15] Kupavskii A., “Degree versions of theorems on intersecting families via stability”, J. Combin. Theory Ser. A., 168 (2019), 272–287 | DOI | MR | Zbl

[16] Pyaderkin M. M., “On the chromatic number of random subgraphs of a certain distance graph”, Discr. Appl. Math., 267 (2019), 209–214 | DOI | MR | Zbl

[17] Raigorodskii A. M., Koshelev M. M., “New bounds on clique-chromatic numbers of Johnson graphs”, Discr. Appl. Math., 283 (2020), 724–729 | DOI | MR | Zbl