vertexCut -- break up a tree at a vertex

Synopsis

Usage:

vertexCut(T,e,l,newl)

vertexCut(T,E,l,newl)
Inputs:
- T, an instance of the type LeafTree,
- e, a set, an edge specified by the set of leaves on one side of it
- E, a list, an edge specified by a list of the leaves on one side of it
- l, a thing, a leaf of the tree
- newl, a thing, the label for a new leaf
Outputs:
- a list, of LeafTrees that are subtrees of T

Description

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

o3 : LeafTree

i4 : P#1

o4 = {{2, 4}, {set {2}}}

o4 : LeafTree

i5 : P#2

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

o5 : LeafTree

Ways to use vertexCut :

vertexCut(LeafTree,List,Thing,Thing)
vertexCut(LeafTree,Set,Thing,Thing)

For the programmer

The object vertexCut is a method function.

vertexCut -- break up a tree at a vertex

Synopsis

Description

See also

Ways to use vertexCut :

For the programmer