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Sbornik: Mathematics, 2012, Volume 203, Issue 10, Pages 1518–1533
DOI: https://doi.org/10.1070/SM2012v203n10ABEH004273 (Mi sm7878) 		 
Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal

K. I. Oblakov, T. A. Oblakova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (296 kB) Russian version article
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DOI: https://doi.org/10.1070/SM2012v203n10ABEH004273
Abstract: 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.
Received: 14.04.2011 and 30.12.2011
Bibliographic databases:
Document Type: Article
UDC: 515.125
MSC: Primary 05C10; Secondary 57M15
Language: English
Original paper language: Russian
Citation: 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”, Sb. Math., 203:10 (2012), 1518–1533
Citation in format AMSBIB
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\by K.~I.~Oblakov, T.~A.~Oblakova
\paper Embeddings of graphs into Euclidean space under which the number of points that belong to a~hyperplane is minimal
\jour Sb. Math.
\yr 2012
\vol 203
\issue 10
\pages 1518--1533
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  • https://doi.org/10.1070/SM2012v203n10ABEH004273
  • https://www.mathnet.ru/eng/sm/v203/i10/p145
    • Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:442
    Russian version PDF:180
    English version PDF:9
    References:61
    First page:19
     
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