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Tony Huynh
Tony Huynh
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Wikipedia does not state that the outerface is convex, but rather that it has a convex boundary. I assume this means that the set consisting of all points inside the boundary is convex. So for example, the outerface has a convex boundary in your two examples. Also, with this defintiondefinition, it is true that every $3$-connected planar graph has a convex drawing (since it is the $1$-skeleton of a $3$-polytope).

Wikipedia does not state that the outerface is convex, but rather that it has a convex boundary. I assume this means that the set consisting of all points inside the boundary is convex. So for example, the outerface has a convex boundary in your two examples. Also, with this defintion, it is true that every $3$-connected planar graph has a convex drawing (since it is the $1$-skeleton of a $3$-polytope).

Wikipedia does not state that the outerface is convex, but rather that it has a convex boundary. I assume this means that the set consisting of all points inside the boundary is convex. So for example, the outerface has a convex boundary in your two examples. Also, with this definition, it is true that every $3$-connected planar graph has a convex drawing (since it is the $1$-skeleton of a $3$-polytope).

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Tony Huynh
Tony Huynh
  • 32.1k
  • 11
  • 112
  • 187

Wikipedia does not state that the outerface is convex, but rather that it has a convex boundary. I assume this means that the set consisting of all points inside the boundary is convex. So for example, the outerface has a convex boundary in your two examples. Also, with this defintion, it is true that every $3$-connected planar graph has a convex drawing (since it is the $1$-skeleton of a $3$-polytope).