In this article, we will show that the complete graph K4 is planar.
Complete Graph: A Complete Graph is a Graph in which all pairs of vertices are directly connected to each other.
K4 is a Complete Graph with 4 vertices.
Planar Graph: A graph is said to be a planar graph if we can draw all its edges in the 2-D plane such that no two edges intersect each other.
The Complete Graph K4 is a Planar Graph. In the above representation of K4, the diagonal edges interest each other. So, it might look like the graph is non-planar. But we can easily redraw K4 such that no two edges interest each other.
In the above K4 graph, no two edges intersect. Thus, K4 is a Planar Graph.
Note: A graph with intersecting edges is not necessarily non-planar. As long as we can re-arrange its edges in the 2-D plane to a configuration in which there’s no intersection of edges, the graph is planar.