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Algorithms for Classes of Graphs with Bounded Expansion

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Graph-Theoretic Concepts in Computer Science (WG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5911))

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Abstract

We overview algorithmic results for classes of sparse graphs emphasizing new developments in this area. We focus on recently introduced classes of graphs with bounded expansion and nowhere-dense graphs and relate algorithmic meta-theorems for these classes of graphs to their analogues for proper minor-closed classes of graphs, classes of graphs with bounded tree-width, locally bounded tree-width and locally excluding a minor.

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References

  1. Arnborg, S., Proskurowski, A., Corneil, D.G.: Forbidden minors characterization of partial 3-trees. Discrete Math. 80, 1–19 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bodlaender, H.L., Deogun, J.S., Jansen, K., Kloks, T., Kratsch, D., Müller, H., Tuza, Z.: Ranking of graphs. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds.) WG 1994. LNCS, vol. 903, pp. 292–304. Springer, Heidelberg (1995)

    Google Scholar 

  3. Bodlaender, H.L., Gilbert, J.R., Hafsteinsson, H., Kloks, T.: Approximating treewidth, pathwidth, frontsize and shortest elimination tree. J. Algorithms 25, 1305–1317 (1996)

    MATH  Google Scholar 

  4. Brodal, G.S., Fagelberg, R.: Dynamic representations of sparse graphs. In: Dehne, F., Gupta, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1999. LNCS, vol. 1663, pp. 342–351. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Courcelle, B.: The monadic second-order logic of graph I. Recognizable sets of finite graphs. Inform. and Comput. 85, 12–75 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dawar, A., Grohe, M., Kreutzer, S.: Locally excluding a minor. In: Proc. LICS 2007, pp. 270–279. IEEE Computer Society Press, Los Alamitos (2007)

    Google Scholar 

  7. DeVos, M., Ding, G., Oporowski, B., Sanders, D.P., Reed, B., Seymour, P.D., Vertigan, D.: Excluding any graph as a minor allows a low tree-width 2-coloring. J. Combin. Theory Ser. B 91, 25–41 (2004)

    MATH  MathSciNet  Google Scholar 

  8. Dvořák, Z.: Assymptotical structure of combinatorial objects, PhD thesis, Charles University (2007)

    Google Scholar 

  9. Dvořák, Z., Král’, D., Thomas, R.: Deciding first order properties for nowhere dense graphs (manuscript) (2009)

    Google Scholar 

  10. Eppstein, D.: Subgraph isomorphism in planar graphs and related problems. In: Proc. SODA 1995, pp. 632–640. ACM&SIAM (1995)

    Google Scholar 

  11. Eppstein, D.: Subgraph isomorphism in planar graphs and related problems. J. Graph Algorithms Appl. 3, 1–27 (1999)

    Article  MathSciNet  Google Scholar 

  12. Eppstein, D.: Diameter and treewidth in minor-closed graph families. Algorithmica 27, 275–291 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Frick, M., Grohe, M.: Deciding first-order properties of locally tree-decomposable structures. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 331–340. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  14. Frick, M., Grohe, M.: Deciding first-order properties of locally tree-decomposable structures. J. ACM 48, 1184–1206 (2001)

    MathSciNet  Google Scholar 

  15. Gaifman, H.: On local and non-local properties. In: Proc. Herbrand Symp. Logic Colloq. North-Holland, Amsterdam (1982)

    Google Scholar 

  16. Kowalik, L.: Adjacency queries in dynamic sparse graphs. Inf. Process. Lett. 102, 191–195 (2007)

    Article  MathSciNet  Google Scholar 

  17. Kowalik, L., Kurowski, M.: Oracles for bounded-length shortest paths in planar graphs. ACM Trans. Algorithms 2, 335–363 (2006)

    Article  MathSciNet  Google Scholar 

  18. Kowalik, L., Kurowski, M.: Short path queries in planar graphs in constant time. In: Proc. STOC 2003, pp. 143–148 (2003)

    Google Scholar 

  19. Nešetřil, J., Ossona de Mendéz, P.: First order properties of nowhere dense structures (manuscript) (2008)

    Google Scholar 

  20. Nešetřil, J., Ossona de Mendéz, P.: Grad and classes with bounded expansion I. Decompositions. European J. Combin. 29, 760–776 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Nešetřil, J., Ossona de Mendéz, P.: Grad and classes with bounded expansion II. Algorithmic aspects. European J. Combin. 29, 777–791 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  22. Nešetřil, J., Ossona de Mendéz, P.: Grad and classes with bounded expansion III. Restricted graph homomorphism dualities. European J. Combin. 29, 1012–1024 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  23. Nešetřil, J., Ossona de Mendéz, P.: Linear time low tree-width partitions and algorithmic consequences. In: Proc. STOC 2006, pp. 391–400 (2006)

    Google Scholar 

  24. Nešetřil, J., Ossona de Mendéz, P.: On nowhere dense graphs (manuscript) (2008)

    Google Scholar 

  25. Nešetřil, J., Ossona de Mendéz, P.: Structural properties of sparse graphs (manuscript) (2008)

    Google Scholar 

  26. Nešetřil, J., Ossona de Mendéz, P.: Tree depth, subgraph coloring and homomorphism bounds. European J. Combin. 27, 1022–1041 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  27. Nešetřil, J., Ossona de Mendéz, P., Wood, D.: Characterizations and examples of graph classes with bounded expansion (manuscript) (2008)

    Google Scholar 

  28. Peleg, D.: Distance-dependent distributed directories. Info. Computa. 103, 270–298 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  29. Robertson, N., Seymour, P.D.: Graph minors V: Excluding a planar graph. J. Combin. Theory Ser. B 41, 92–114 (1986)

    Article  MathSciNet  Google Scholar 

  30. Robertson, N., Seymour, P.D.: Graph Minors XX. Wagner’s conjecture. J. Combin. Theory Ser. B 92, 325–357 (2004)

    MathSciNet  Google Scholar 

  31. Seese, D.: Linear time computable problems and first-order descriptions. Math. Structu. Comput. Sci. 6, 505–526 (1996)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague 1, Czech Republic

    Zdeněk Dvořák & Daniel Král’

Authors
  1. Zdeněk Dvořák
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  2. Daniel Král’
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Editor information

Editors and Affiliations

  1. CNRS - LIRMM, 161 rue Ada, 34392, Montpellier Cedex 5, France

    Christophe Paul

  2. LIAFA, case 7014, Université Paris Diderot, 75205, Paris Cedex 13, France

    Michel Habib

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Dvořák, Z., Král’, D. (2010). Algorithms for Classes of Graphs with Bounded Expansion. In: Paul, C., Habib, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11409-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-11409-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11408-3

  • Online ISBN: 978-3-642-11409-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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