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Treewidth of Grid Subsets

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References

  1. N. Alon, G. Ding, B. Oporowski and D. Vertigan: Partitioning into graphs with only small components, Journal of Combinatorial Theory, Ser. B 87 (2003), 231–243.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Baker: Approximation algorithms for NP-complete problems on planar graphs, Journal of the ACM (JACM) 41 (1994), 153–180.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Chekuri and J. Chuzhoy: Polynomial bounds for the grid-minor theorem, in: Proceedings of the 46th Annual ACM Symposium on Theory of Computing, STOC’ 14, New York, NY, USA, 2014, ACM, 60–69.

    Google Scholar 

  4. J. Chuzhoy: Excluded grid theorem: Improved and simplified, in: Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC’ 15, New York, NY, USA, 2015, ACM, 645–654.

    Chapter  Google Scholar 

  5. L. Cowen, W. Goddard and C. E. Jesurum: Defective coloring revisited, Journal of Graph Theory 24 (1997), 205–219.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  7. G. Ding, B. Oporowski, D. P. Sanders and D. Vertigan: Surfaces, tree-width, clique-minors, and partitions, Journal of Combinatorial Theory, Ser. B 79 (2000), 221–246.

    MATH  Google Scholar 

  8. Z. Dvořák: Sublinear separators, fragility and subexponential expansion, European Journal of Combinatorics 52, Part A (2016), 103–119.

    Article  MathSciNet  MATH  Google Scholar 

  9. K. Edwards, D. Y. Kang, J. Kim, S.-i. Oum and P. Seymour: A relative of hadwiger’s conjecture, SIAM J. Discrete Math. 29 (2015), 2385–2388.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Gale: The game of Hex and the Brouwer fixed-point theorem, The American Mathematical Monthly 86 (1979), 818–827.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Liu and S. Oum: Partitioning h-minor free graphs into three subgraphs with no large components, Electronic Notes in Discrete Mathematics 49 (2015), 133–138.

    Article  MATH  Google Scholar 

  13. J. Matouőek and A. PřívĕtivŶ: Large monochromatic components in two-colored grids, SIAM Journal on Discrete Mathematics 22 (2008), 295–311.

    Article  MathSciNet  MATH  Google Scholar 

  14. N. Robertson and P. D. Seymour: Graph Minors. III. Planar tree-width, J. Combin. Theory, Ser. B 36 (1984), 49–64.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. N. Robertson, P. D. Seymour and R. Thomas: Quickly excluding a planar graph, J. Combin. Theory, Ser. B 62 (1994), 323–348.

    MathSciNet  MATH  Google Scholar 

  17. P. D. Seymour and R. Thomas: Graph searching and a min-max theorem for treewidth, Journal of Combinatorial Theory, Ser. B 58 (1993), 22–33.

    MATH  Google Scholar 

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Correspondence to Zdeněk Dvořák.

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Berger, E., Dvořák, Z. & Norin, S. Treewidth of Grid Subsets. Combinatorica 38, 1337–1352 (2018). https://doi.org/10.1007/s00493-017-3538-5

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  • DOI: https://doi.org/10.1007/s00493-017-3538-5

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