google-deepmind / google-deepmind/formal-conjectures
Graph embedding conjecture
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Description
### What is the conjecture
Is there a constant C such that for every graph G on n vertices and m edges, there is a triangulation of, say, S^6, that contains G as a subcomplex and has C(n+m) faces?
Remarks: S^6 is just an example. It can be any fixed manifold (though surfaces are boring, so let's say of dimension at least 3).
### Prerequisites needed
This conjecture touches on various subjects. It is related to the random generation of regular simplicial complexes, the enumeration of triangulations of manifolds, as well as the generation of high-dimensional expanders.
### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)
* ams-XX
### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else
Contributor guide
Research direction
The issue does not name a file, test, or entry point. Start by reading the repository's existing formalized conjectures and conventions for graph and manifold statements; done means the graph embedding conjecture is added in the repository's accepted formal form.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Needs clarification
- Newbie friendliness
- 30/100