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Application of a directed almost tree

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Problem Detail: 

Is there anything interesting to say about an "almost BST" with directed edges? Is there a domain where this structure naturally arises? I'm imagining a tree like the one below, but it would of course be more interesting if the tree were deeper with just a few of these strange edges.

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I found this article on circuit rank which uses the term "almost tree", but it talks about circuits in undirected and directed graphs. What I'm describing is not a cycle.

Asked By : Julian Cienfuegos
Answered By : Yuval Filmus

What you are looking for are directed acyclic graphs (DAGs). If you want your DAG to have a unique "root", then you can ask for a DAG with a single source. DAGs are very useful in many branches of computer science.

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