Просмотр кода страницы Reach-preservable graph

'''Reach-preservable graph''' ---  сохраняющий достижимость граф. 

Given a '' spanning tree'' <math>T</math> of a graph <math>G</math>, a vertex <math>v \in V(G)</math>
is called ''' reach-preserving''' if the distance <math>d_{T}(v,w) =
d_{G}(v,w)</math> for all <math>w</math> in <math>G</math>.
A graph is called ''' reach-preservable graph''' if each of its spanning trees has a
reach-preserving vertex.

By definition, it is clear that all trees are reach-preservable, and
any cycle is reach-preservable. Furthermore, we can deduce that
connected '' unicyclic'' graphs are reach-presevable.