Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Independent transversals in r-partite graphs
Discrete Mathematics
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
The extremal function for complete minors
Journal of Combinatorial Theory Series B
Two Short Proofs Concerning Tree-Decompositions
Combinatorics, Probability and Computing
Independent Transversals and Independent Coverings in Sparse Partite Graphs
Combinatorics, Probability and Computing
Odd Independent Transversals are Odd
Combinatorics, Probability and Computing
Quickly deciding minor-closed parameters in general graphs
European Journal of Combinatorics
Independent transversals in locally sparse graphs
Journal of Combinatorial Theory Series B
Hitting all maximum cliques with a stable set using lopsided independent transversals
Journal of Graph Theory
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Large-treewidth graph decompositions and applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Lower bounds on the complexity of MSO1 model-checking
Journal of Computer and System Sciences
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Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an @?x@? grid minor is exponential in @?. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order@? in a graph G is a set of paths in G whose intersection graph is bipartite and contains a K"@?-minor. For example, the rows and columns of the @?x@? grid are a grid-like-minor of order @?+1. We prove that polynomial treewidth forces a large grid-like-minor. In particular, every graph with treewidth at least c@?^4log@? has a grid-like-minor of order @?. As an application of this result, we prove that the Cartesian product G@?K"2 contains a K"@?-minor whenever G has treewidth at least c@?^4log@?.