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Let T= V,E) be a tree with n nodes such that each node v is associated with a value-weight pair (valv,wv), where the value valv is a real number and the weight wv is a positive integer.
Let be a tree with root, and let be a sequence of positive integers.
Let T be a tree with at least four vertices, none of which has degree 2, embedded in the plane.
Corollary 2.5 Let T be a tree with n vertices and diameter d ≥ 3. Then μ 1 ( T ) < n − 0.5.
Let G be a tree with a diametrical path P. If (ABC(G) - r (G)) is minimum among trees, then there is at most one vertex outside P in G. Suppose to the contrary that there are at least two vertices outside P in G. Assume that (P = v_{0} v_{1} cdots v_{d}).
Let G be a tree with n leaf nodes, vertex set V(G), and edge set E(G).
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In Central Park, when we went out to look at those trees, there was a tree with a rough-legged hawk.
Civility is a tree with deep roots, and without the roots, it can't last.
A James space J(T) is defined on a general tree T, that is, a tree with arbitrary width and height any ordinal.
We present a PTAS for this problem, when the underlying graph is a tree with the degrees of the vertices bounded by a constant, e.g. binary tree.
The final result is a tree with decision nodes and leaf nodes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com