Sparsity-certifying graph decompositions

Graphs and Combinatorics

Volumn 25, Issue 2, 2009, Pages 219-238

  Streinu, Ileana ^a   Theran, Louis ^b  

^a SMITH COLLEGE   (United States)

^b University of Massachusetts Amherst   (United States)

Author keywords

Matroids; Sprase graphs; Tree decompositions

Indexed keywords

EID: 67649646668     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00373-008-0834-4     Document Type: Article

References (24)

1. Berg, A.R., Jordán, T.: Algorithms for graph rigidity and scene analysis. In: Proc. 11th European Symposium on Algorithms (ESA '03), LNCS, 2832, 78-89 (2003)
2. Crapo, H.: On the generic rigidity of plane frameworks. Tech. Rep. 1278, Institut de recherche d'informatique et d'automatique (1988)
3. Edmonds, J.: Minimum partition of a matroid into independent sets. J. Res. Nat. Bur. Standards Sect. B 69B, 67-72 (1965)
4. Edmonds, J.: Submodular functions, matroids, and certain polyhedra. In: Combinatorial Optimization-Eureka, You Shrink!, no. 2570 in LNCS, pp. 11-26. Springer (2003) (Pubitemid 137631146)
5. Gabow, H.N.: A matroid approach to finding edge connectivity and packing arborescences. J. Comp. Sys. Sci. 50, 259-273 (1995)
6. Gabow, H.N., Westermann, H.H.: Forests, frames, and games: Algorithms for matroid sums and applications. Algorithmica 7(1), 465-497 (1992)
7. Haas, R.: Characterizations of arboricity of graphs. Ars Combinatorica 63, 129-137 (2002) (Pubitemid 37306703)
8. Haas, R., Lee, A., Streinu, I., Theran, L.: Characterizing sparse graphs by map decompositions. J. Comp. Math. Comb. Comput 62, 3-11 (2007) (Pubitemid 47394044)
9. Hendrickson, B.: Conditions for unique graph realizations. SIAM J. Comput. 21(1), 65-84 (1992)
10. Jacobs, D.J., Hendrickson, B.: An algorithm for two-dimensional rigidity percolation: the pebble game. J. Comput. Phy. 137, 346-365 (1997) (Pubitemid 127170000)
11. Laman, G.: On graphs and rigidity of plane skeletal structures. J. Eng. Math. 4, 331-340 (1970)
12. Lee, A., Streinu, I.: Pebble game algorihms and sparse graphs. Discrete Mathematics 308(8), 1425-1437 (2008) (Pubitemid 351186413)
13. Lee, A., Streinu, I., Theran, L.: Finding and maintaining rigid components. In: Proc. Canadian Conference of Computational Geometry. Windsor, Ontario (2005). http://cccg.cs.uwindsor.ca/papers/72.pdf
14. Lee, A., Streinu, I., Theran, L.: Graded sparse graphs and matroids. J. Uni Comput Sci 13(10), (2007a and 2007b)
15. Lee, A., Streinu, I., Theran, L.: The slider-pinning problem. In: Proceedings of the 19th Canadian Conference on Computational Geometry (CCCG'07) (2007)
16. Lovász, L.: Combinatorial Problems and Exercises. Akademiai Kiado and North- Holland, Amsterdam (1979)
17. Nash-Williams, C.S.A.: Decomposition of finite graphs into forests. J. Lond Math. Soc. 39, 12 (1964)
18. Oxley, J.G.: Matroid theory. The Clarendon Press, Oxford University Press, New York (1992)
19. Roskind, J., Tarjan, R.E.: A note on finding minimum cost edge disjoint spanning trees. Math. Oper. Res. 10(4), 701-708 (1985)
20. Streinu, I., Theran, L.: Combinatorial genericity and minimal rigidity. In: SCG '08: Proceedings of the twenty-fourth annual Symposium on Computational Geometry, pp. 365-374. ACM, New York, NY, USA (2008)
21. Tay, T.S.: Rigidity of multigraphs I: linking rigid bodies in n-space. J. Comb. Theor. Ser. B 26, 95-112 (1984)
22. Tay, T.S.: A new proof of Laman's theorem. Graphs and Combinatorics 9, 365-370 (1993)
23. Tutte, W.T.: On the problem of decomposing a graph into n connected factors. J. Lond. Math. Soc. 142, 221-230 (1961)
24. Whiteley, W.: The union of matroids and the rigidity of frameworks. SIAM J. Dis. Math 1(2), 237-255 (1988)