Let G = (V,w) be a weighted undirected graph with m edges. The cut dimension of G is the dimension of the span of the characteristic vectors of the minimum cuts of G, viewed as vectors in \{0,1\}^m.
Nov 10, 2020
On the Contact Dimension of Graphs. P. Frankl; H. Maehara · Discrete & computational geometry (1988). Volume ...
The smallest dimension n for which such an embedding exists is called the contact dimension of G, and is denoted by cd(G). Here we present some bounds on the ...
The smallest dimensionn needed to representG in such a way is called the contact dimension ofG and it is denoted by cd(G).
Mar 1, 1988 · On the contact dimensions of graphs. Published: 01 March 1988. Volume 3, pages 89–96, (1988); Cite this article. Download PDF · Discrete ...
TL;DR: A survey of graph properties related to geometric representations, construction methods for geometric representations and their applications in proofs ...
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A simple short proof of the Johnson-Lindenstrauss lemma (concerning nearly isometric embeddings of finite point sets in lower-dimensional spaces) is given.
The contact graph of a packing of translates of a convex body in Euclidean d-space E-d is the simple graph whose vertices are the members of the packing, and ...
A simple proof of the Galvin-Ramsey property of the class of all finite graphs and a dimension of a graph.
Aug 3, 2020 · In this paper, we derive an asymptotically tight lower bound on the broadcast dimension of an acyclic graph in the number of vertices.