next | previous | forward | backward | up | top | index | toc | Macaulay2 website
PhylogeneticTrees :: vertexCut

vertexCut -- break up a tree at a vertex



Vertices of a tree of class LeafTree do not have explicit names. Therefore a vertex v is specified by naming an edge e incident to v, and leaf l on the opposite side of the edge as v.

The function outputs the subtrees of T obtained by deleting the vertex v from T and then re-adding v to each of the resulting subtrees as a new leaf. The new leaf on each subtree is adjacent to the edge previously adjacent to v on T. Each subtree has a copy of the vertex labeled newl, but their edge sets form a partition of the edge set of T.

Each subtree in P has one leaf that was not a leaf of T, and therefore previously unlabeled. The label for this new leaf is input as newl.

i1 : T = leafTree(4,{{0,1}})

o1 = {{0, 1, 2, 3}, {set {0, 1}, set {0}, set {1}, set {2}, set {3}}}

o1 : LeafTree
i2 : P = vertexCut(T, set {0,1}, 0, 4);
i3 : P#0

o3 = {{2, 4}, {set {2}}}

o3 : LeafTree
i4 : P#1

o4 = {{3, 4}, {set {3}}}

o4 : LeafTree
i5 : P#2

o5 = {{0, 1, 4}, {set {0}, set {1}, set {4}}}

o5 : LeafTree

See also

Ways to use vertexCut :

For the programmer

The object vertexCut is a method function.