Geodesic
On minimal hard classes of graphs
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 6, pp. 43-51.

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

We consider the notions of a minimal hard class of graphs and a boundary class of graphs. We prove that there is no minimal hard classes for problem of recognition belonging to a hereditary class. We point out boundary and minimal hard classes of graphs for the list-ranking problems. These classes of graphs are the first examples of minimal hard classes and the first examples of hard boundary classes. Bibl. 9.
Keywords: computational complexity, minimal hard class, boundary class, recognition of hereditary property, list-ranking problems. 
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D. S. Malyshev. On minimal hard classes of graphs. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 6, pp. 43-51. http://geodesic.mathdoc.fr/item/DA_2009_16_6_a3/

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

[2] Kharari F., Teoriya grafov, Mir, M., 1982, 301 pp.

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

[5] Breu H., Kirkpatrick D. G., “Unit disk graph recognition is NP-hard”, Comput. Geometry, 9 (1998), 3–24 | DOI | MR | Zbl

[6] Dereniowski D., “The complexity of list ranking of trees”, Ars Combinatoria, 86 (2008), 97–114 | MR

[7] Golumbic M. C., Jamison R. E., “The edge intersection graphs of paths in trees”, J. Combinatorial Theory B, 38 (1985), 8–22 | DOI | MR | Zbl

[8] Jamison R. E., “Coloring parameters associated with rankings of graphs”, Congressus Numerantum, 164 (2003), 111–127 | MR | Zbl

[9] Roussopoulos N., “A $\max\{m,n\}$ algorithm for determining the graph $H$ from its line graph $G$”, Information Processing Lett., 2:4 (1973), 108–112 | DOI | MR | Zbl