Good spanning tree

In the mathematical field of graph theory, a good spanning tree [1]

of an embedded planar graph

is a rooted spanning tree of

whose non-tree edges satisfy the following conditions.

ϕ

be a plane graph.

be a rooted spanning tree of

to a vertex

divides the children of

, into two groups; the left group

and the right group

is in group

and denoted by

appears before the edge

in clockwise ordering of the edges incident to

when the ordering is started from the edge

Similarly, a child

is in the group

and denoted by

appears after the edge

in clockwise order of the edges incident to

when the ordering is started from the edge

is called a good spanning tree[1] of

if every vertex

satisfies the following two conditions with respect to

In monotone drawing of graphs,[2] in 2-visibility representation of graphs.

[1] Every planar graph

contains a good spanning tree.

A good spanning tree and a suitable embedding can be found from

contain a good spanning tree.