# Tag Info

Accepted

### Minimal good cover of the torus

You can't do any better than $7$. This follows from Karoubi, Max; Weibel, Charles A., On the covering type of a space, Enseign. Math. (2) 62, No. 3-4, 457-474 (2016). ZBL1378.55002. in particular ...
• 33.3k
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• 5,436
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• 37.4k
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### Is König's Property for graphs inheritable from finite subgraphs?

(Just making my comment an answer as suggested.) If every finite subgraph of $G$ satisfies Kőnig's Property, then $G$ has no odd cycles and is thus bipartite. Aharoni (König's Duality Theorem For ...
• 1,526
Accepted

### Covering all except one of the purple intersection points of $n$ red and $m$ blue lines efficiently

The very nice paper "Cayley-Bacharach theorems and conjectures" by David Eisenbud, Mark Green, and Joe Harris (http://www.ams.org/journals/bull/1996-33-03/S0273-0979-96-00666-0/home.html) gives an ...
• 4,735

### How to "lift" a transitive group action on a manifold?

The Palais theorem assumes that the manifold $\tilde M$ is compact. The positive answer gives proposition 6 of the Onishchik book "Topology of transitive transformation groups". It ...
Accepted

### How to "lift" a transitive group action on a manifold?

If $G$ is connected, take its Lie algebra, acting as vector fields on $M$. Lift the vector fields by the covering map. There is a unique connected Lie group $\tilde{G}$ acting on $\tilde{M}$ whose Lie ...
• 23.4k
Accepted

### Finding a minimum covering of a polygon with interesting shapes

There is a recent paper by Tobias Christ that extends the covering work I cited in the comments, and work by Andrejz Lingas, to triangles, one of the problems left unresolved by that earlier work. ...
• 145k
### Minimal covering sets in families of sets intersecting in at most $1$ point
I think I can do one case. Assume that $A_i\subseteq S$, $|A_i|=\aleph_0$ for $i\in I$, and $|A_i\cap A_j|\leq 1$ for $i\neq j$. By a theorem in the paper P. Komjáth: Families close to disjoint ones,...