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Felix Goldberg
Felix Goldberg
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Completing a tree to ana 2-connected outerplanar graph

Let $T$ be a given (finite) tree.

Question 1: Is it always possible to add edges to $T$ to obtain ana $2$-connected outerplanar supergraph $G$?

Question 2: If the answer to Question #1 is negative, can the trees for which it is possible be characterized?

Question 3( Defect form of Question 1): Let $v \in V(T)$$T$ be a designatedrooted tree with root vertex $v_{0} \in V(T)$. Is it always possible to add edges to $T$ to obtain a $2$-connected planar graph $G$ with a plane embedding in which $v$$v_{0}$ is the only internal vertex?

Completing a tree to an outerplanar graph

Let $T$ be a given (finite) tree.

Question 1: Is it always possible to add edges to $T$ to obtain an outerplanar supergraph $G$?

Question 2: If the answer to Question #1 is negative, can the trees for which it is possible be characterized?

Question 3( Defect form of Question 1): Let $v \in V(T)$ be a designated vertex. Is it always possible to add edges to $T$ to obtain a planar graph $G$ with a plane embedding in which $v$ is the only internal vertex?

Completing a tree to a 2-connected outerplanar graph

Let $T$ be a given (finite) tree.

Question 1: Is it always possible to add edges to $T$ to obtain a $2$-connected outerplanar supergraph $G$?

Question 2: If the answer to Question #1 is negative, can the trees for which it is possible be characterized?

Question 3( Defect form of Question 1): Let $T$ be a rooted tree with root vertex $v_{0} \in V(T)$. Is it always possible to add edges to $T$ to obtain a $2$-connected planar graph $G$ with a plane embedding in which $v_{0}$ is the only internal vertex?

Source Link
Felix Goldberg
Felix Goldberg
  • 7k
  • 4
  • 31
  • 55

Completing a tree to an outerplanar graph

Let $T$ be a given (finite) tree.

Question 1: Is it always possible to add edges to $T$ to obtain an outerplanar supergraph $G$?

Question 2: If the answer to Question #1 is negative, can the trees for which it is possible be characterized?

Question 3( Defect form of Question 1): Let $v \in V(T)$ be a designated vertex. Is it always possible to add edges to $T$ to obtain a planar graph $G$ with a plane embedding in which $v$ is the only internal vertex?