Return to Question

When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of convex drawing is from Wikipedia.

In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

Surprisingly, is the outer face not convex in second example?

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that the unbounded face is the complement of a convex set.

So I'm confused by the definition of convex drawing where boundary of the outer face is also convex. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs

When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of convex drawing is from Wikipedia.

In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

Surprisingly, the outer face is not convex in the second example.

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that the unbounded face is the complement of a convex set.

So I'm confused by the definition of convex drawing where boundary of the outer face is also convex. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs

When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of convex drawing is from Wikipedia.

In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

Surprisingly, is the outer face not convex in second the example?

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that the unbounded face is the complement of a convex set.

So I'm confused by the definition of convex drawing where boundary of the outer face is also convex. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs

When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of convex drawing is from Wikipedia.

In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

Surprisingly, is the outer face not convex in second example?

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that the unbounded face is the complement of a convex set.

So I'm confused by the definition of convex drawing where boundary of the outer face is also convex. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs

When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of [convex drawing ][1]is from Wikipedia.

In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

[![enter image description here][2]][2]

Surprisingly, is the outer face not convex in second the example? [![enter image description here][3]][3]

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that the unbounded face is the complement of a convex set.

So I'm confused by the definition of convex drawing where boundary of the outer face is also convex. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs

[1]: https://en.wikipedia.org/wiki/Convex_drawing#:~:text=In%20graph%20drawing%2C%20a%20convex,face)%20have%20a%20convex%20boundary. [2]: https://i.sstatic.net/O7KQH.png [3]: https://i.sstatic.net/jaqfW.png

When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of convex drawing is from Wikipedia.

In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

Surprisingly, is the outer face not convex in second the example?

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that the unbounded face is the complement of a convex set.

So I'm confused by the definition of convex drawing where boundary of the outer face is also convex. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs