Geodesic
Embeddings of graphs into Euclidean space under which the number of points that belong to a~hyperplane is minimal
Sbornik. Mathematics, Tome 203 (2012) no. 10, pp. 1518-1533

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The paper is devoted to the characteristic of a graph that is the minimal (over all embeddings of the graph into a space of given dimension) number of points that belong to the same hyperplane. Upper and lower estimates for this number are given that linearly depend on the dimension of the space. For trees a more precise upper estimate is obtained, which asymptotically coincides with the lower one for large dimension of the space. Bibliography: 9 titles.
Keywords: graph, embedding, hyperplane. 
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     author = {K. I. Oblakov and T. A. Oblakova},
     title = {Embeddings of graphs into {Euclidean} space under which the number of points that belong to a~hyperplane is minimal},
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K. I. Oblakov; T. A. Oblakova. Embeddings of graphs into Euclidean space under which the number of points that belong to a~hyperplane is minimal. Sbornik. Mathematics, Tome 203 (2012) no. 10, pp. 1518-1533. http://geodesic.mathdoc.fr/item/SM_2012_203_10_a4/