For every , all sufficiently large integers have the property that every with contains a corner in an integer grid. The tripartite graph encoding of a grid turns the absence of a corner into a family of many edge-disjoint triangles but only quadratically many total triangles in a graph, contradicting the triangle removal lemma.
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Corners theorem, often referred to in the context of graph theory and combinatorial geometry, generally deals with conditions on the arrangement of points or vertices in a specific geometric or combinatorial setting. The theorem states that given a finite set of points in the plane, one can find a subset of these points such that certain geometric or combinatorial properties hold, often involving the vertices (or corners) of a configuration.