On two-colour perfect colourings of circular graphs
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 1, pp. 80-92.

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

We consider perfect colourings of a certain class of infinite graphs called circular graphs. It is shown that every such perfect colouring yields a perfect colouring of an $n$-dimensional infinite lattice which has the same parameters as the original colouring. A construction that produces two-colour perfect colourings of circular graphs is proposed and the parameters of perfect colourings given by the construction are enumerated. Bibl. 12.
Keywords: perfect colouring, circular graph
Mots-clés : equitable partition.
@article{DA_2009_16_1_a4,
     author = {D. B. Khoroshilova},
     title = {On two-colour perfect colourings of circular graphs},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {80--92},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2009_16_1_a4/}
}
TY  - JOUR
AU  - D. B. Khoroshilova
TI  - On two-colour perfect colourings of circular graphs
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2009
SP  - 80
EP  - 92
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2009_16_1_a4/
LA  - ru
ID  - DA_2009_16_1_a4
ER  - 
%0 Journal Article
%A D. B. Khoroshilova
%T On two-colour perfect colourings of circular graphs
%J Diskretnyj analiz i issledovanie operacij
%D 2009
%P 80-92
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2009_16_1_a4/
%G ru
%F DA_2009_16_1_a4
D. B. Khoroshilova. On two-colour perfect colourings of circular graphs. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 1, pp. 80-92. http://geodesic.mathdoc.fr/item/DA_2009_16_1_a4/

[1] Avgustinovich S. V., Borodin O. V., Frid A. E., “Distributivnye raskraski ploskikh triangulyatsii minimalnoi stepeni 5”, Diskret. analiz i issled. operatsii. Ser. 1, 8:3 (2001), 3–16 | MR

[2] Vizing V. G., “Distributivnaya raskraska vershin grafa”, Diskret. analiz i issled. operatsii, 2:4 (1995), 3–12 | MR | Zbl

[3] Efremova E. M., Molodykh E. A., Parametry sovershennykh raskrasok beskonechnoi kubicheskoi reshëtki v dva tsveta, Doklad na seminare “Teoriya kodirovaniya”, IM SO RAN, 2003

[4] Puzynina S. A., “Periodichnost sovershennykh raskrasok beskonechnoi pryamougolnoi reshëtki”, Diskret. analiz i issled. operatsii. Ser. 1, 11:1 (2004), 79–92 | MR | Zbl

[5] Puzynina S. A., “Sovershennye raskraski vershin grafa $G(\mathbb Z^2)$ v tri tsveta”, Diskret. analiz i issled. operatsii. Ser. 2, 12:1 (2005), 37–54 | MR

[6] Fon-Der-Flaass D. G., “Sovershennye 2-raskraski 12-mernogo kuba, dostigayuschie granitsy korrelyatsionnoi immunnosti”, Sib. elektron. mat. izv., 4 (2007), 292–295 | Zbl

[7] Fon-Der-Flaass D. G., “Sovershennye 2-raskraski giperkuba”, Sib. mat. zhurn., 48:4 (2007), 923–930 | MR | Zbl

[8] Kharari F., Teoriya grafov, Mir, M., 1973, 299 pp. | MR

[9] Axenovich M. A., “On multiple coverings of the infinite rectangular grid with balls of constant radius”, Discrete Maths., 268:1–3 (2003), 31–49 | DOI | MR

[10] Agustini E., Costa S. I. R., Muniz M., Palazzo R., “Graphs, tesselations, and perfect codes on flat tori”, IEEE Transactions on Information Theory, 50:10 (2004), 2363–2377 | DOI | MR

[11] Godsil C., “Equitable partitions”, Combinatorics. Paul Erdös is Eighty, V. 1, Keszthely (Hungary), 1993, 173–192 | MR | Zbl

[12] Krotov D. S., Perfect 9-colorings of $\mathbb Z^2$, ArXiv.org (to appear)