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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 ...

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 ...

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 ...

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 ...