Laminar structure of ptolemaic graphs and its applications

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3827 LNCS, Issue , 2005, Pages 186-195

  Uehara, Ryuhei ^a   Uno, Yushi ^b  

^a JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

^b Osaka Prefecture University   (Japan)

Author keywords

Algorithmic graph theory; Data structure; Hamiltonian cycle; Intersection model; Ptolemaic graphs

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; DATA STRUCTURES; HAMILTONIANS; PROBLEM SOLVING; TREES (MATHEMATICS);

ALGORITHMIC GRAPH THEORY; HAMILTONIAN CYCLE; INTERSECTION MODELS; PTOLEMAIC GRAPHS;

GRAPH THEORY;

EID: 33744960937     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11602613_20     Document Type: Conference Paper

References (19)

1. H.-J, Bandelt and H.M. Mulder. Distance-Hereditary Graphs, J. of Combinatorial Theory, Series B, 41; 182-208, 1986.
2. A. Brandstädt, V.B. Le, and J.P. Spinrad. Graph Classes: A Survey. SIAM, 1999.
3. A. Bretscher, D. Corneil, M. Habib, and C. Paul. A Simple Linear Time LexBFS Cograph Recognition Algorithm. In Graph-Theoretic Concepts in Computer Science (WG 2003), pages 119-130. LNCS Vol. 2880, Springer-Verlag, 2003.
4. H.J. Broersma, E. Dahlhaus, and T. Kloks. A linear time algorithm for minimum fill-in and treewidth for distance hereditary graphs. Discrete Applied Mathematics, 99:367-400, 2000.
5. M.-S. Chang, S.-Y. Hsieh, and G.-H. Chen. Dynamic Programming on Distance-Hereditary Graphs. In Proceedings of 8th International Symposium on Algorithms and Computation (ISAAC '97), pages 344-353. LNCS Vol. 1350, Springer-Verlag, 1997.
6. D.G. Corneil. Lexicographic Breadth First Search - A Survey. In Graph-Theoretic Concepts in Computer Science (WG 2004), pages 1-19. LNCS Vol. 3353, Springer-Verlag, 2004.
7. G. Damiand, M. Habib, and C. Paul. A Simple Paradigm for Graph Recognition: Application to Cographs and Distance Hereditary Graphs. Theoretical Computer Science, 263:99-111, 2001.
8. A. D'Atri and M. Moscarini. Distance-Hereditary Graphs, Steiner Trees, and Connected Domination. SIAM J. on Computing, 17(3):521-538, 1988.
9. F. Gavril. Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph. SIAM J. on Computing, 1(2):180-187, 1972.
10. M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Annals of Discrete Mathematics 57. Elsevier, 2nd edition, 2004.
11. P.L. Hammer and F. Maffray. Completely Separable Graphs. Discrete Applied Mathematics, 27:85-99, 1990.
12. E. Howorka. A Characterization of Distance-Hereditary Graphs. Quart. J. Math. Oxford (2), 28:417-420, 1977.
13. E. Howorka. A Characterization of Ptolemaic Graphs. J. of Graph Theory, 5:323-331, 1981.
14. R.-W. Hung and M.-S. Chang. Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs. Theoretical Computer Science, 341:411-440, 2005.
15. B. Korte and J. Vygen. Combinatorial Optimization, volume 21 of Algorithms and Combinatorics. Springer, 2000.
16. D.J. Rose, R.E. Tarjan, and G.S. Lueker. Algorithmic Aspects of Vertex Elimination on Graphs. SIAM J. on Computing, 5(2):266-283, 1976.
17. J.P. Spinrad. Efficient Graph Representations. American Mathematical Society, 2003.
18. R. Uehara and Y. Uno. Efficient Algorithms for the Longest Path Problem. In 15th Annual International Symposium on Algorithms and Computation (ISAAC 2004), pages 871-883. LNCS Vol.3341, Springer-Verlag, 2004.
19. H.-G. Yeh and G.J. Chang. Centers and medians of distance-hereditary graphs. Discrete Mathematics, 265:297-310, 2003.