On finding augmenting graphs

Discrete Applied Mathematics

Volumn 156, Issue 13, 2008, Pages 2517-2529

  Lozin, Vadim V ^a   Milanič, Martin ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b BIELEFELD UNIVERSITY   (Germany)

Author keywords

Augmenting graph; Independent set; Polynomial time algorithm

Indexed keywords

CURVE FITTING; IMAGE RETRIEVAL; NUCLEAR PROPULSION; POLYNOMIAL APPROXIMATION; POLYNOMIALS; SET THEORY; SOLUTIONS;

AUGMENTING GRAPH; EFFICIENT SOLUTIONS; GENERAL APPROACH; GRAPH G; INDEPENDENT SET; LINE GRAPHS; MAXIMUM INDEPENDENT SET; MAXIMUM MATCHING; NP-HARD; OF GRAPHS; POLYNOMIAL-TIME; POLYNOMIAL-TIME ALGORITHM; POLYNOMIAL-TIME ALGORITHMS;

GRAPH THEORY;

EID: 49749102368     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2008.03.008     Document Type: Article

References (17)

1. Alekseev V.E. The effect of local constraints on the complexity of determination of the graph independence number. Combinatorial-Algebraic Methods in Applied Mathematics (1982), Gorkiy Univ. Press, Gorky 3-13 (in Russian)
2. Alekseev V.E. A polynomial algorithm for the independent set problem in fork-free graphs. Discrete Appl. Math. 135 (2004) 3-16
3. Alekseev V.E., and Lozin V.V. Augmenting graphs for independent sets. Discrete Appl. Math. 145 (2004) 3-10
4. Berge C. Two theorems in graph theory. Proc. Nat. Acad. Sci. USA 43 (1957) 842-844
5. 5-free graphs. Discrete Appl. Math. 131 (2003) 567-575
6. T. Denley, The independence number of graphs with large odd girth, Electron. J. Combinatorics, 1:Research Paper 9, 1994, 12 pp
7. Edmonds J. Path, trees, and flowers. Canad. J. Math. 17 (1965) 449-467
8. Gerber M.U., Hertz A., and Lozin V.V. Stable sets in two subclasses of banner-free graphs. Discrete Appl. Math. 132 (2004) 121-136
9. Gerber M.U., Hertz A., and Lozin V.V. Finding augmenting chains in graphs without a skew star. J. Combin. Theory Ser.B 96 (2006) 352-366
10. Hall P. On representatives of subsets. J. Lond. Math. Soc. 10 (1935) 26-30
11. M.M. Halldórsson, Approximating discrete collections via local improvements, in: Proc. of the Sixth SIAM-ACM Symposium on Discrete Algorithms San Francisco, CA, 1995, pp. 160-169
12. Hertz A., Lozin V., and Schindl D. Finding augmenting chains in extensions of claw-free graphs. Inform. Process. Lett. 86 (2003) 311-316
13. Lovász L., and Plummer M.D. Matching Theory. Ann. Discrete Math vol. 29 (1986), North-Holland Publishing Co, Amsterdam Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, xxvii+544 pp
14. 5- and banner-free graphs. European J. Oper. Res. 125 (2000) 292-297
15. Minty G.J. On maximal independent sets of vertices in claw-free graphs. J. Combin. Theory Ser. B 28 (1980) 284-304
16. 6-free graphs. Discrete Appl. Math. 92 (1999) 177-191
17. Sbihi N. Algorithme de recherche d'un stable de cardinalité maximum dans un graphe sans étoile. Discrete Math. 29 (1980) 63-76