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realization of a graph (Definition)

A realization of a graph $G$ in a topological space $X$ is an injective map $\rho:G\to X$ such that $G$ with the graph topology is homeomorphic to $\rho(G)$ with the subspace topology. Of particular interest are realizations of $G$ in 3-dimensional Euclidean space, where each of the edges is a line segment, and where no 4 points of $G$ are coplanar.




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"realization of a graph" is owned by rmilson. [ full author list (3) | owner history (2) ]
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See Also: subdivision, graph topology

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Cross-references: coplanar, points, line segment, edges, Euclidean space, subspace topology, homeomorphic, graph topology, map, injective, topological space

This is version 4 of realization of a graph, born on 2002-03-07, modified 2006-10-13.
Object id is 2774, canonical name is Realization.
Accessed 3273 times total.

Classification:
AMS MSC05C99 (Combinatorics :: Graph theory :: Miscellaneous)

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