Prove that complete graph K4 is planar

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.

Complete Graph K4

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.

Planer Graph of Complete Graph K4

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.


Planer Graph

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