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Let T be a tree on at least four vertices.
T be a tree on ((k+1)n) vertices.
Let G be a tree on (n ge4) vertices with a diametrical path P. If there is at most one vertex outside P in G, then ABC (G) - r (G) gefrac{n-1}{sqrt{2}} - biggllfloor frac{n}{2} biggrrfloor with equality if and only if (G cong P_{n}).
But as you'll see, danger can come in many forms (there could even be a tree on the side the road!).
Let U be a tree on G.
Let T be a tree on ∪ i S i. Assume that S i = A i ∪ X, with A i ∩ A j =∅ for all i≠ j, that t i = T| S i (the subtree of T induced by taxon set S i ), and that every short quartet of T is in some S i. Then SCM applied to { t1, t2,…, t k } returns T, independent of the order in which the trees are merged.
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"I don't want to be a tree for dogs to piss on," says the tree.
"Here's a tree on life-support systems".
"There was a tree on my leg and I couldn't see my baby anymore".
I paid to get the bulk of it taken out, but there was a tree on the street that didn't have a flower bed.
Jason Watkins said his father woke him and said, "Two things: there's no power, and there's a tree on our car".
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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