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Jacob.Z.Lee
Jacob.Z.Lee
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A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded. enter image description here

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $\tilde{G}$$ {G'}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt(\tilde{G})=bt(G).$$bt( {G'})=bt(G).$

I will appreciate it if someone could give any suggestions.

A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded. enter image description here

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $\tilde{G}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt(\tilde{G})=bt(G).$

I will appreciate it if someone could give any suggestions.

A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded. enter image description here

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $ {G'}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt( {G'})=bt(G).$

I will appreciate it if someone could give any suggestions.

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Jacob.Z.Lee
Jacob.Z.Lee
  • 767
  • 3
  • 11

A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded. enter image description here

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $\tilde{G}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt(\tilde{G})=bt(G).$

I will appreciate it if someone could give any suggestions.

A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded.

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $\tilde{G}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt(\tilde{G})=bt(G).$

I will appreciate it if someone could give any suggestions.

A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded. enter image description here

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $\tilde{G}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt(\tilde{G})=bt(G).$

I will appreciate it if someone could give any suggestions.

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Jacob.Z.Lee
Jacob.Z.Lee
  • 767
  • 3
  • 11

A simple equality for book embedding of two graphs

A book embedding of a graph $G$ consists of placing the vertices of $G$ on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is the minimum number of pages in which the graph $G$ can be embedded.

Recently, I wondered whether the following result is right:

Let $ {G}$ be a simple connected graph, a graph $\tilde{G}$ is from the graph $G$ by adding a new vertex on any edge $e$ of $G$, then $bt(\tilde{G})=bt(G).$

I will appreciate it if someone could give any suggestions.