Embedding products of graphs into Euclidean spaces
نویسندگان
چکیده
منابع مشابه
Embedding Products of Graphs into Euclidean Spaces
For any collection of graphs G1, . . . , GN we find the minimal dimension d such that the product G1 × · · · ×GN is embeddable into R . In particular, we prove that (K5) and (K3,3) are not embeddable into R, where K5 and K3,3 are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is the reduction to a problem from so-called Ramsey link theory: we s...
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(m 2) of nontrivial connected graphs G i and the n-dimensional base B de Bruijn graph D = D B (n), we investigate whether or not there exists a spanning subgraph of D which is isomorphic to G. We show that G is never a spanning subgraph of D when n is greater than three or when n equals three and m is greater than two. For n = 3 and m = 2, we can show for wide classes of graphs that G cannot be...
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Integration of concepts for the parallelization of image processing algorithms into parallel compiler technology. Abstract Given a Cartesian product G = G 1 : : : G m (m 2) of nontrivial connected graphs G i and the n{dimensional base B de Bruijn graph D = D B (n), it is investigated whether or not G is a spanning subgraph of D. Special attention is given to graphs G 1 : : : G m which are relev...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2003
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm179-3-1