Sets of lattice points which contain a maximal number of edges

Clements, G. F.

doi:10.1090/S0002-9939-1971-0270923-7

Sets of lattice points which contain a maximal number of edges
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by G. F. Clements PDF

Proc. Amer. Math. Soc. 27 (1971), 13-15 Request permission

Abstract:

How should one select an $l$-element subset of a rectangular array of lattice points (points with integral coordinates) in $n$-dimensional Euclidean space so as to include the largest possible number of edges (pairs of points differing in exactly one coordinate)? It is shown that the generalized Macaulay theorem due to the author and B. Lindström contains the (known) solution.

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