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Table 1 Rooted triplets as constrained unrooted triplets

From: Auto-validating von Neumann rejection sampling from small phylogenetic tree spaces

Rooted and Clocked Trees, it := (it0, it1), i ∈ {1, 2, 3}

Unrooted Trees 4t := (4t1, 4t2, 4t3)

Labeled Tree

Newick Representation of it

4 t 1

4 t 2

4 t 3

1t := (1t0, 1t1)

((H:1t1, C:1t1):1t0, G:1t0 + 1t1))

1 t 1

1 t 1

1t1 + 1t0 + 1t0

2t := (2t0, 2t1)

((C:2t1, G:2t1):2t0, H:2t0 + 2t1))

2t1 + 2t0 + 2t0

2 t 1

2 t 1

3t := (3t0, 3t1)

((H:3t1, G:3t1):3t0, C:3t0 + 3t1))

3 t 1

3t1 + 3t0 + 3t0

3 t 1

  1. Any labeled, rooted and clocked tree with three leaves can be represented as a constrained unrooted tree according to the tabulated transformation.