Geodesic
Continued sets of boundary classes of graphs for colorability problems
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 41-51.

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

We point out continued sets of boundary classes of graphs for the 3-vertex-colorability problem and for the 3-edge-colorability problem. These are the first examples of graph problems with sets of boundary classes of such cardinality. Bibl. 9.
Keywords: boundary classes of graphs, 3-colorability problems, continued sets of boundary classes. 
@article{DA_2009_16_5_a4,
     author = {D. S. Malyshev},
     title = {Continued sets of boundary classes of graphs for colorability problems},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {41--51},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2009_16_5_a4/}
}
TY  - JOUR
AU  - D. S. Malyshev
TI  - Continued sets of boundary classes of graphs for colorability problems
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2009
SP  - 41
EP  - 51
VL  - 16
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2009_16_5_a4/
LA  - ru
ID  - DA_2009_16_5_a4
ER  - 
%0 Journal Article
%A D. S. Malyshev
%T Continued sets of boundary classes of graphs for colorability problems
%J Diskretnyj analiz i issledovanie operacij
%D 2009
%P 41-51
%V 16
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2009_16_5_a4/
%G ru
%F DA_2009_16_5_a4
D. S. Malyshev. Continued sets of boundary classes of graphs for colorability problems. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 41-51. http://geodesic.mathdoc.fr/item/DA_2009_16_5_a4/

[1] Alekseev V. E., Malyshev D. S., “Kriterii granichnosti i ego primeneniya”, Diskret. analiz i issled. operatsii, 15:6 (2008), 3–10 | MR

[2] Malyshev D. S., “O beskonechnosti mnozhestva granichnykh klassov v zadache o rebernoi 3-raskraske”, Diskret. analiz i issled. operatsii, 16:1 (2009), 37–43 | MR

[3] Alekseev V. E., “On easy and hard hereditary classes of graphs with respect to the independent set problem”, Discrete Appl. Math., 132 (2004), 17–26 | DOI | MR

[4] Alekseev V. E., Korobitsyn D. V., Lozin V. V., “Boundary classes of graphs for the dominating set problem”, Discrete Math., 285 (2004), 1–6 | DOI | MR | Zbl

[5] Alekseev V. E., Boliac R., Korobitsyn D. V., Lozin V. V., “NP-hard graph problems and boundary classes of graphs”, Theoret. Comput. Sci., 389 (2007), 219–236 | DOI | MR | Zbl

[6] Bodlaender H. L., “Dynamic programming on graphs with bounded treewidth”, Automata, languages and programming, Proc. (Tampere, 1988), Lect. Notes in Comput. Sci., 317, Springer–Verl., Berlin, 1988, 105–118 | MR

[7] Holyer I., “The NP-completeness of edge-coloring”, SIAM J. Comput., 10:4 (1981), 718–720 | DOI | MR | Zbl

[8] Kochol M., Lozin V., Randerath B., “The 3-colorability problem on graphs with maximum degree four”, SIAM J. Comput., 32:5 (2003), 1128–1139 | DOI | MR | Zbl

[9] Lozin V. V., Rautenbach D., “On the band-, tree- and clique-width of graphs with bounded vertex degree”, Discrete Math., 18 (2004), 195–206 | DOI | MR | Zbl