Halin's grid theorem

[1] It was published by Rudolf Halin (1965), and is a precursor to the work of Robertson and Seymour linking treewidth to large grid minors, which became an important component of the algorithmic theory of bidimensionality.

An example of a graph with a thick end is provided by the hexagonal tiling of the Euclidean plane.

For example, some of its rays form Hamiltonian paths that spiral out from a central starting vertex and cover all the vertices of the graph.

Because it has infinitely many pairwise disjoint rays, all equivalent to each other, this graph has a thick end.

Although the precise relation between treewidth and grid minor size remains elusive, this result became a cornerstone in the theory of bidimensionality, a characterization of certain graph parameters that have particularly efficient fixed-parameter tractable algorithms and polynomial-time approximation schemes.