References
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.
B. Baker: Approximation algorithms for NP-complete problems on planar graphs, Journal of the ACM (JACM) 41 (1994), 153–180.
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.
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.
L. Cowen, W. Goddard and C. E. Jesurum: Defective coloring revisited, Journal of Graph Theory 24 (1997), 205–219.
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.
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.
Z. Dvořák: Sublinear separators, fragility and subexponential expansion, European Journal of Combinatorics 52, Part A (2016), 103–119.
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.
D. Eppstein: Diameter and treewidth in minor-closed graph families, Algorithmica 27 (2000), 275–291.
D. Gale: The game of Hex and the Brouwer fixed-point theorem, The American Mathematical Monthly 86 (1979), 818–827.
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.
J. Matouőek and A. PřívĕtivŶ: Large monochromatic components in two-colored grids, SIAM Journal on Discrete Mathematics 22 (2008), 295–311.
N. Robertson and P. D. Seymour: Graph Minors. III. Planar tree-width, J. Combin. Theory, Ser. B 36 (1984), 49–64.
N. Robertson and P. D. Seymour: Graph Minors. V. Excluding a planar graph, J. Combin. Theory, Ser. B 41 (1986), 92–114.
N. Robertson, P. D. Seymour and R. Thomas: Quickly excluding a planar graph, J. Combin. Theory, Ser. B 62 (1994), 323–348.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Berger, E., Dvořák, Z. & Norin, S. Treewidth of Grid Subsets. Combinatorica 38, 1337–1352 (2018). https://doi.org/10.1007/s00493-017-3538-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00493-017-3538-5