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Results tagged with trees
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user 46140
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.
1
vote
Maximize this score function on a directed tree
If $a \to b$ then $s(b) \ge s(a)$, so an $a$ which maximises $s(a)$ subject to $\operatorname{dep} a \le N$ has $\operatorname{dep} a = N$.
If $k_1 < k_2$ and $a_{k_1} < a_{k_2}$ then the word obtaine …
- 7,226
2
votes
About the maximum number of leaves adjacent to a vertex in a tree
This allows us to do most of the work with rooted trees. … and the second term counts bicentroidal trees. …
- 7,226
5
votes
Accepted
Bijectively counting labeled trees by number of leaves
If you identify a function $f: [n-1] \to [n]$ with the Prüfer code $(f(1), f(2), \ldots, f(n-1))$ then it corresponds to an unrooted labelled tree on $n+1$ vertices in which the label $n+1$ is a leaf. …
- 7,226
2
votes
Accepted
Completing a tree to a 2-connected outerplanar graph
Yes. Pick an arbitrary vertex to be the root. Consider the sequence of vertices $v_1, v_2, \ldots$ produced by a pre-order traversal of the rooted tree, adding edges $v_i - v_{i+1}$ where they don't a …
- 7,226
3
votes
Accepted
Stern-Brocot tree and subtree
The second half is already given in the question, so really what you're asking is whether $$b(2n-1)=b(2n-3)+b(n-1)-2(b(2n-3)\bmod b(n-1))$$
But as noted in OEIS (quoted with relabelling),
Moshe Newma …
- 7,226