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Maximum independent sets in graphs of low degree
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Source Symposium on Discrete Algorithms archive
Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms table of contents
New Orleans, Louisiana
Pages: 874 - 880  
Year of Publication: 2007
ISBN:978-0-898716-24-5
Authors
Vadim Lozin  Rutgers University, Piscat-away NJ
Martin Milanič  Rutgers University, Piscataway NJ
Sponsors
: SIAM Activity Group on Discrete Mathematics
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
Publisher
Society for Industrial and Applied Mathematics  Philadelphia, PA, USA
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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.

Collaborative Colleagues:
Vadim Lozin: colleagues
Martin Milanič: colleagues