**24**

votes

**9**answers

3k views

### Is the empty graph a tree?

This is a boring, technical question that I stumbled upon while making a contribution to Sage. I would still like to hear a constructive answer so hopefully the question does not get closed.
The ...

**13**

votes

**1**answer

516 views

### Are the asymptotics of A003238 known?

Sequence A003238 of the OEIS counts ``rooted trees with $n$ vertices in which vertices at the same level have the same degree.'' The sequence, $a$, begins
1, 1, 2, 3, 5, 6, 10, 11, 16, ...
and it is ...

**5**

votes

**2**answers

230 views

### Can we have a $\kappa$-Suslin tree where $\kappa$ is above a measurable cardinal?

Question: Can we have a set theory in which there exists a $\kappa$-Suslin tree with $\kappa$ larger than the least measurable cardinal?
A $\kappa$-Suslin tree is a tree with levels indexed by ...

**3**

votes

**1**answer

189 views

### Partitioning a binary tree into vertex-disjoint subtrees

Say we have a labeled, binary unrooted tree $T$, i.e. each node has either 1 or 3 neighbors.
Denote by $L(T)$ the set of leaves (degree-one nodes) of $T$.
For some $L \subseteq L(T)$, denote by ...