What is a planar triangulation?

What is a planar triangulation?

A planar triangulation is a (multi)-graph drawn in the plane so that every face is a triangle. For various reasons, it is better to consider rooted triangulations. A root is defined as a triangle in the triangulation, together with a distinguished ordering of the vertices of the triangle.

What is triangulation graph?

A triangulated graph is a graph in which for every cycle of length ℓ > 3, there is an edge joining two nonconsecutive vertices. In this paper we study triangulated graphs and show that they play an important role in the elimination process.

Which bipartite graphs are planar?

Every planar graph whose faces all have even length is bipartite. Special cases of this are grid graphs and squaregraphs, in which every inner face consists of 4 edges and every inner vertex has four or more neighbors. The complete bipartite graph on m and n vertices, denoted by Kn,m is the bipartite graph.

What is planar graph in discrete mathematics?

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.

Is the Petersen graph planar?

Because it is nonplanar, it has at least one crossing in any drawing, and if a crossing edge is removed from any drawing it remains nonplanar and has another crossing; therefore, its crossing number is exactly 2. Each edge in this drawing is crossed at most once, so the Petersen graph is 1-planar.

Which of the following graphs is planar?

Concept: A planar graph is a graph in which no two edges cross each other. A vertex coloring of a graph is an assignment of colors to the vertices of a graph such that adjacent vertices have different colors. So, both K4 and Q3 are planar.

Is K4 2 a planar?

A graph G= (V, E) is said to be planar if it can be drawn in the plane so that no two edges of G intersect at a point other than a vertex. Such a drawing of a planar graph is called a planar embedding of the graph. For example, K4 is planar since it has a planar embedding as shown in figure 1.8.