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The paper Seven Trees in One exhibits a "very explicit bijection" $T^7\cong T$. It is perhaps a bit cumbersome because it requires separating into five cases based on how the seven trees look in the first four levels of depth. A proof is present too. Disclaimer: I haven't read it. Another paper Objects of Categories as Complex Numbers discusses the ...

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The problem is listed in Lovasz's problem book. This is problem 4 in chapter 4. The original solution is attributed to J. W. Moon, but I haven't managed to find the article describing this. The proof is fairly complicated so it's not a surprise that it's omitted from the editorial. EDIT: Seems like Igor Pak shared the original book as well, although the ...

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As was mentioned https://en.wikipedia.org/wiki/Arborescence_%28graph_theory%29 is likely what you are looking for. A graph is a spanning tree if it is a tree (acyclyic, connected graph) that touches each node. In Directed Spanning trees it looks like either you choose a node, mark it as the root and build a tree that is defined as being a single path from ...

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There isn't necessarily a single term that satisfies all of your criteria under all discussions. https://en.wikipedia.org/wiki/Rooted_graph Rooted DAG (directed acyclic graph), often (almost always) has the condition that the graph is reachable from the root vertex (you would technically qualify that the first time in a paper if you wanted to be formal). ...

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Let your points-to-be-connected be $A=(0,0)$, $B=(4,3)$, $C=(-3,4)$, and $D=(1,7)$, the vertices of a square. I think you get your tree by letting $E=(0,4)$, $F=(1,3)$, drawing $AE$, $CE$, $DF$, and $BF$, and then drawing a horizontal line to join $AE$ and $DF$. But the vertical location of that horizontal segment, and of the inner points it creates, are not ...

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