Good spanning tree
In the mathematical field of graph theory, a good spanning tree T {\displaystyle T} of an embedded planar graph G {\displaystyle G} is a rooted spanning tree of G {\displaystyle G} whose non-tree edges satisfy the following conditions. there is no non-tree edge ( u , v ) {\displaystyle (u,v)} where u {\displaystyle u} and v {\displaystyle v} lie on a path from the root of T {\displaystyle T} to a leaf, the edges incident to a vertex v {\displaystyle v} can be divided by three sets X v , Y v {\displaystyle X_{v},Y_{v}} and Z v {\displaystyle Z_{v}} , where, X v {\displaystyle X_{v}} is a set of non-tree edges, they terminate in red zone Y v {\displaystyle Y_{v}} is a set of tree edges, they are children of v {\displaystyle v} Z v {\displaystyle Z_{v}} is a set of non-tree edges, they terminate in green zone == Formal definition == Source: Let G ϕ {\displaystyle G_{\phi }} be a plane graph.