# Questions tagged [trees]

A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.

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### Minimum spanning tree and projection

Let $G$ be a graph of $n$ arcs and let $x\in \mathbb{R}^n$. I want to compute the orthogonal projection of $x$ onto the set of radial graphs with $k$ roots contained in $G$ (or a forest with $k$ root) ...
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### Terminology for a subtree of a rooted tree with a path boundedness property

I'm not a graph theorist, so I apologize if some of the following terminology isn't quite correct. Let $(T,f,v_0)$ be a complete degree $d$ rooted tree (definition at the end). Definition. Let $m\ge0$....
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### Is there a formula for the number of trees with this extra condition?

A tree $G$ on $n$ vertices $V=\{v_1,...,v_n\}$ is a connected undirected graph which is acyclic. For each tree $G$ one can split the set of vertices $V$ into two disjoint subsets $U,W \subset V$ such ...
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### Estimating the largest radius making each ball in a finite metric space into a tree

Motivation: Let $n$ be a positive integer and $(X,d)$ be an $n$-point metric space. Clearly, $(X,d)$ need not be a metric tree (e.g. take for example the discrete metric on $\{0,1,2\}$. Conversely, ...
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### "Meritocratic" pyramid schemes

There have been a couple of times in my life when people from multi-level marketing organizations attempted to recruit me. I listened to what they had to say, and both times I did not get involved ...