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Consider a binary tree constructed as the following. Given a node with a some value $x$, I construct two children nodes each having value $l(x)$ and $r(x)$ respectively. I repeat the same on the ...

This is a cross-post from math.stackexchange.com$^{[1]}$, since the bounty there didn't lead to any new insights. For reference, The Frog game is the generalization of the Frog Jumping (see it on ...

I want to know if there exists a positive constant $c$ such that: Given rooted binary tree, $T$, with root $r$ and height $h$ (not necessarily a full tree), the following holds: $$\frac{[\sum_{v \in ...

Embedding different graphs, especially binary trees, in the hypercube has a huge literature. However, I could not find anything if we restrict the embedding to be monotone. So I would like to ...

Let $T$ be a complete infinite rooted binary tree. Is it possible to remove (infinitely many) subtrees of $T$ and get a subgraph $G$ such that: $G$ has no complete subtrees (the graph below any ...