Geodesic
The perfect colorings of circulant graphs with a large number of colors
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 188-195
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An infinite circulant graph with a continuous set of distances is a graph, whose set of vertices is the set of integers, and two vertices $i$ and $j$ are adjacent if $|i-j| \in \{1,2,...,n\}$. We study perfect colorings of such graph with $k$ colors for $k$ at least $3n+3$. A complete description of them is obtained.
Keywords: perfect coloring, $k$-motley fragment.
Mots-clés : infinite circulant graph 
@article{SEMR_2024_21_1_a18,
     author = {M. A. Lisitsyna and S. V. Avgustinovich},
     title = {The perfect colorings of circulant graphs with a large number of colors},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {188--195},
     year = {2024},
     volume = {21},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a18/}
}
TY  - JOUR
AU  - M. A. Lisitsyna
AU  - S. V. Avgustinovich
TI  - The perfect colorings of circulant graphs with a large number of colors
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 188
EP  - 195
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a18/
LA  - ru
ID  - SEMR_2024_21_1_a18
ER  - 
%0 Journal Article
%A M. A. Lisitsyna
%A S. V. Avgustinovich
%T The perfect colorings of circulant graphs with a large number of colors
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 188-195
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a18/
%G ru
%F SEMR_2024_21_1_a18
M. A. Lisitsyna; S. V. Avgustinovich. The perfect colorings of circulant graphs with a large number of colors. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 188-195. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a18/

[1] D.B. Khoroshilova, “On the parameters of perfect 2-colorings of circulant graphs”, Diskretn. Anal. Issled. Oper., 18:6 (2011), 82–89 | MR | Zbl

[2] D.B. Khoroshilova, “On circular perfect two-color colorings”, Diskretn. Anal. Issled. Oper., 16:1 (2009), 80–92 | MR | Zbl

[3] O.G. Parshina, “Perfect 2-colorings of infinite circulant graphs with a continuous set of distances”, J. Appl. Ind. Math., 8:3 (2014), 357–361 | DOI | MR | Zbl

[4] O.G. Parshina, M.A. Lisitsyna, “The perfect 2-colorings of infinite circulant graphs with a continuous set of odd distances”, Sib. Èlectron. Math. Izv., 17 (2020), 590–603 | DOI | MR | Zbl

[5] M.A. Lisitsyna, O.G. Parshina, “Perfect colorings of the infinite circulant graph with distances 1 and 2”, J. Appl. Industr. Math., 11:3 (2017), 381–388 | DOI | MR | Zbl

[6] O.G. Parshina, “Perfect $k$-colorings of infinite circulant graphs with a continuous set of distances”, Groups and Graphs, Algorithms and Automata, Int. Conf. PhD Summer Sch. (Aug. 9–15, 2015, Yekaterinburg, Russia), eds. A. Makhnev et al., 2015, 80 | MR

[7] V.D. Plaksina, P.A. Shcherbina, “New perfect colorings of infinite circulant graphs with continuous sets of distanses”, Sib. Èlectron Mat. Izv., 18:1 (2021), 530–533 | DOI | MR | Zbl

[8] M.A. Lisitsyna, S.V. Avgustinovich, “Test fragments of perfect colorings of circulant graphs”, Sib. Èlectron Mat. Izv., 20:2 (2023), 638–645 | MR

[9] D. Cvetković, M. Doob, H. Sachs, Spectra of graphs. Theory and applications, J. A. Barth Verlag, Leipzig, 1995 | MR | Zbl