Lesson plan
Graph flattenability
Flattenability in some d -dimensional normed vector space is a property of graphs which states that any embedding, or drawing, of the graph in some high dimension d' can be "flattened" down to live in d -dimensions, such that the distances between pairs of points connected by edges are preserved. A graph G is d -flattenable if every distance constraint system (DCS) with G as its constraint graph has a d -dimensional framework. Flattenability was first called realizability, but the name was changed to avoid confusion with a graph having some DCS with a d -dimensional framework. Flattenability has connections to structural rigidity, tensegrities, Cayley configuration spaces, and a variant of the graph realization problem.
Article summary
Flattenability in some d -dimensional normed vector space is a property of graphs which states that any embedding, or drawing, of the graph in some high dimension d' can be "flattened" down to live in d -dimensions, such that the distances between pairs of points connected by edges are preserved. A graph G is d -flattenable if every distance constraint system (DCS) with G as its constraint graph has a d -dimensional framework. Flattenability was first called realizability, but the name was changed to avoid confusion with a graph having some DCS with a d -dimensional framework. Flattenability has connections to structural rigidity, tensegrities, Cayley configuration spaces, and a variant of the graph realization problem.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.