On the extension of bipartite to parity graphs

Discrete Applied Mathematics

Volumn 95, Issue 1-3, 1999, Pages 181-195

  Cicerone, Serafino ^a   Di Stefano, Gabriele ^a  

^a UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Maximum weighted clique problem; Maximum weighted independent set problem; Parity graphs; Recognition problem; Split composition

Indexed keywords

EID: 0041777786     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00074-8     Document Type: Article

References (28)

1. G.S. Adhar, S. Peng, Parallel algorithms for cographs and parity graphs with applications, J. Algorithms 11 (2) (1990) 252-284.
2. G. Ausiello, A. D'Atri, M. Moscarini, Chordality properties on graphs and minimal conceptual connection in semantic data models, J. Comput. System Sci. 33 (2) (1986) 179-202.
3. H.J. Bandelt, A. D'Atri, M. Moscarini, H.M. Mulder, A. Schultze, Operations on distance hereditary graphs, Technical Report 226, CNR, Istituto di Analisi dei Sistemi e Informatica del CNR, Rome, Italy, 1988.
4. H.J. Bandelt, M. Mulder, Distance-hereditary graphs, J. Combin. Theory, Ser. B 41 (2) (1986) 182-208.
5. H.J. Bandelt, M. Mulder, Metric characterization of parity graphs, Discrete Math. 91 (1991) 221-230.
6. A. Bouchet, Transforming trees by successive local complementations, J. Graph Theory 4 (1988) 196-207.
7. M. Burlet, J. Fonlupt, Polynomial algorithm to recognize meyniel graphs, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, number 21 Ann. Discrete Math. North-Holland, Amsterdam, 1984, pp. 225-252.
8. M. Burlet, J.P. Uhry, Parity graphs, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, number 21 Ann. Discrete Math. North-Holland, Amsterdam, 1984, pp. 253-277.
9. S. Cicerone, G. Di Stefano, On the equivalence in complexity among basic problems on bipartite and parity graphs, in: eighth International Symposium on Algorithms and Computation (ISAAC'97), vol. 1350, Lecture Notes in Computer Science, Springer, Berlin, December 1997, pp. 354-363.
10. S. Cicerone, G. Di Stefano, Graph classes between parity and distance-hereditary graphs, in: First Discrete Mathematics and Theoretical Computer Science (DMTCS'96), Combinatorics, Complexity, and Logic, Springer, Berlin, 1996, pp. 168-181.
11. S. Cicerone, G. Di Stefano, Port and node support to compact routing, Technical Report R.97-17, Dipartimento di Ingegneria Elettrica, Università di L'Aquila, L'Aquila, Italy, 1997.
12. D.G. Corneil, H. Lerchs, L. Stewart-Burlingham, Complement reducible graphs, Discrete Appl. Math. 3 (1981) 163-174.
13. W.H. Cunningham, Decomposition of directed graphs, SIAM J. Alg. Disc. Meth. 3 (1982) 214-228.
14. E. Dahlhaus, An efficient parallel recognition algorithm for parity graphs, in: O. Abou-Rabia et al. (Eds.), ICCI '93, 1993, pp. 82-86.
15. E. Dahlhaus, Efficient parallel and linear time sequential split decomposition, in: 14th Foundations of Software Technology and Theoretical Computer Science (FSTTCS'94), vol. 880, Lecture Notes in Computer Science, 1994.
16. G. Di Stefano, A routing algorithm for networks based on distance-hereditary topologies, in: Third International Colloquium on Structural Information and Communication Complexity (SIROCCO'96), 1996.
17. A.H. Esfahanian, O.R. Oellermann, Distance-hereditary graphs and multidestination message-routing in multicomputers, J. Combin. Math. Combin. Comput. 13 (1993) 213-222.
18. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, NY, 1980.
19. M. Grötschel, L. Lovász, A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1 (1981) 169-197.
20. P.L. Hammer, F. Maffray, Completely separable graphs, Discrete Appl. Math. 27 (1990) 85-99.
21. F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
22. 5/2) algorithm for maximum matchings in bipartite graphs, SIAM J. Comput. 2 (4) (1973) 225-231.
23. E. Howorka, A characterization of ptolemaic graphs, J. Graph Theory 5 (1981) 323-331.
24. L. Lovasz, A characterization of perfect graphs, J. Combin. Theory Ser. B 13 (1972) 95-98.
25. H. Meyniel, The graphs whose odd cicles have at least two cords, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, number 21 Ann. Discrete Math., North-Holland, Amsterdam, 1984, pp. 115-119.
26. R.H. Möhring, F.J. Radermacher, Substitution decomposition for discrete structure and connection with combinatorial optimization, Ann. Discrete Math. 19 (1984) 257-356.
27. T. Przytycka, D.G. Corneil, Parallel algorithms for parity graphs, J. Algorithms 12 (1) (1991) 96-109.
28. H. Sachs, On the berge conjecture concerning perfect graphs, in: Combinatorial Structures and their Applications, Gordon and Breach, New York, 1970, pp. 377-384.