Geodesic
Chromatic uniqueness of atoms in lattices of complete multipartite graphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 3, pp. 22-29 
V. A. Baranskii; T. A. Koroleva. Chromatic uniqueness of atoms in lattices of complete multipartite graphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 3, pp. 22-29. http://geodesic.mathdoc.fr/item/TIMM_2007_13_3_a1/
@article{TIMM_2007_13_3_a1,
     author = {V. A. Baranskii and T. A. Koroleva},
     title = {Chromatic uniqueness of atoms in lattices of complete multipartite graphs},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {22--29},
     year = {2007},
     volume = {13},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_3_a1/}
}
TY  - JOUR
AU  - V. A. Baranskii
AU  - T. A. Koroleva
TI  - Chromatic uniqueness of atoms in lattices of complete multipartite graphs
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2007
SP  - 22
EP  - 29
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2007_13_3_a1/
LA  - ru
ID  - TIMM_2007_13_3_a1
ER  - 
%0 Journal Article
%A V. A. Baranskii
%A T. A. Koroleva
%T Chromatic uniqueness of atoms in lattices of complete multipartite graphs
%J Trudy Instituta matematiki i mehaniki
%D 2007
%P 22-29
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2007_13_3_a1/
%G ru
%F TIMM_2007_13_3_a1

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A new approach is suggested to the study of the chromatic uniqueness of complete multipartite graphs. The approach is based on the natural lattice order introduced for such graphs. It is proved that atoms with nonelemental partite sets are chromatically unique in the lattice of complete $t$-partite $n$-graphs for any given positive integers $n$ and $t$.

[1] Read R. C., “An introduction to chromatic polynomials”, J. Comb. Theory, 4 (1968), 52–71 | DOI | MR

[2] Asanov M. O., Baranskii V. A., Rasin V. V., Diskretnaya matematika: grafy, matroidy, algoritmy, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001, 288 pp.

[3] Farrell E. J., “On chromatic coefficients”, Discrete Math., 29 (1980), 257–264 | DOI | MR | Zbl

[4] Baranskii V. A., Vikharev S. V., “O khromaticheskikh invariantakh dvudolnykh grafov”, Izv. Ural. gos. un-ta. Matematika i mekhanika, 7:36 (2005), 25–34 | MR

[5] Koh K. M., Teo K. L., “The search for chromatically unique graphs”, Graphs Combin., 6 (1990), 259–285 | DOI | MR | Zbl

[6] Read R. C., Tutte W. T., “Chromatic polynomials”, Selected Topics in Graph Theory III, Academic Press, New York, 1988, 15–42 | MR

[7] Koh K. M., Teo K. L., “The search for chromatically unique graphs II”, Discrete Math., 172 (1997), 59–78 | DOI | MR | Zbl

[8] Chia G. L., “Some problems on chromatic polynomials”, Discrete Math., 172 (1997), 39–44 | DOI | MR | Zbl

[9] Zhao H., Chromaticity and adjoint polynomials of graphs, Wöhrmann Print Service, Zutphen, 2005

[10] Endryus G., Teoriya razbienii, Nauka, M., 1982, 256 pp. | MR

[11] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982, 456 pp. | MR

[12] Chao C. Y., G. A. Novacky Jr., “On maximally saturated graphs”, Discrete Math., 41 (1982), 139–143 | DOI | MR | Zbl