Bifalgorithm post · Brisk · Chapter 1

What is a free tree?

What is a free tree? (Brisk · Chapter 1) — "A tree is really nothing but a simplification of a graph. There are two kinds of trees in the world: free trees, an…

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  • A tree is a simplification of a graph.
  • A tree retains the essential structure of a graph.
  • There are two kinds of trees.
  • Free trees
  • Rooted trees
  • A free tree is a connected graph with no cycles.
  • Every node in a free tree is reachable from every other node.
  • There is only one way to get from one node to another.
  • A free tree looks like a graph but is more skeletal than the WWII France graph.
  • A free tree contains nothing extra in this sense.
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What is a free tree?

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Brisk

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"A tree is really nothing but a simplification of a graph. There are two kinds of trees in the world: free trees, and rooted trees. A free tree is just a connected graph with no cycles. Every node is reachable from the others, and there’s only one way to get anywhere. It looks just like a graph (and it is) but unlike the WWII France graph, it’s more skeletal. This is because in some sense, a free tree doesn’t contain anything “extra.”"

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