|
ABSTRACT
We study computational complexity of the maximum independent set problem on graphs of bounded vertex degree. In general, this problem is NP-hard. However, under certain restrictions it becomes polynomial-time solvable. We identify three graph properties to which the complexity of the problem is sensible.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
| |
1
|
V. E. Alekseev, On the number of maximal independent sets in graphs from hereditary classes, Combinatorial-algebraic methods in discrete optimization, University of Nizhny Novgorod, (1991) 5--8 (in Russian).
|
| |
2
|
|
| |
3
|
|
| |
4
|
|
| |
5
|
A. Brandstädt, C. Hoàng, On Clique Separators, Nearly Chordal Graphs, and the Maximum Weight Stable Set Problem, Proceedings IPCO 2005, Berlin, LNCS 3509, 265--275.
|
| |
6
|
|
| |
7
|
M. Farber, M. Hujter and Zs. Tuza, An upper bound on the number of cliques in a graph, Networks 23 (1993) 207--210.
|
| |
8
|
F. Gavril, Algorithms for minimum coloring, maximum clique, minimum covering by cliques, and maximum independent set of a chordal graph, SIAM J. Comput. 1 (1972) 180--187.
|
| |
9
|
M. G. Garey and D. S. Johnson, The rectilinear Steiner tree problem is NP-complete, SIAM J. Appl. Math. 32 (1977) no. 4, 826--834.
|
| |
10
|
M. Grötschel, L. Lovász and A. Schrijver, Polynomial algorithms for perfect graphs, Ann. Discrete Math. 21 (1984) 325--356.
|
| |
11
|
|
 |
12
|
|
| |
13
|
G. J. Minty, On maximal independent sets of vertices in claw-free graphs, J. Combinatorial Theory, Ser. B, 28 (1980) 284--304.
|
| |
14
|
|
| |
15
|
D. Nakamura and A. Tamura, A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph, J. Oper. Res. Soc. Japan 44 (2001) 194--204.
|
| |
16
|
E. Prisner, Graphs with few cliques, Graph theory, combinatorics, and algorithms, Vol. 1, 2 (Kalamazoo, MI, 1992), 945--956, Wiley-Intersci. Publ., Wiley, New York, 1995.
|
| |
17
|
N. Sbihi, Algorithme de recherche d'un stable de cardinalité maximum dans un graphe sans étoile, Discrete Math. 29 (1980) 53--76.
|
| |
18
|
R. E. Tarjan, Decomposition by clique separators. Discrete Math., 55 (1985) 221--232.
|
| |
19
|
S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirakawa, A new algorithm for generating all the maximal independent sets, SIAM J. Computing, 6 (1977) 505--517.
|
|