# How do you test the planarity of a graph?

## How do you test the planarity of a graph?

Planarity criteria Kuratowski’s theorem that a graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 (the complete graph on five vertices) or K3,3 (the utility graph, a complete bipartite graph on six vertices, three of which connect to each of the other three).

What is planarity of a graph?

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.

### How will you detect planarity?

Detection of Planarity of a Graph

1. DETECTION OF PLANARITY OF A GRAPH : If a given graph G is planar or non planar is an important problem.
2. Elementary Reduction :
3. Step 1 : Since a disconnected graph is planar if and only if each of its components is planar, we need consider only one component at a time.

What are the criteria for planarity testing graphs?

Planarity criteria. Planarity testing algorithms typically take advantage of theorems in graph theory that characterize the set of planar graphs in terms that are independent of graph drawings. These include Kuratowski’s theorem that a graph is planar if and only if it does not contain a subgraph that is a subdivision of K5…

## How to test if a graph is planar?

Characterisation of Planar Graphs: First we introduce planar graphs, and give its characterisation alongwith some simple properties. Planarity Testing: Next, we give an algorithm to test if a given graph is planar using the properties that we have uncovered.

Which is the output of a planarity testing algorithm?

Rather than just being a single Boolean value, the output of a planarity testing algorithm may be a planar graph embedding, if the graph is planar, or an obstacle to planarity such as a Kuratowski subgraph if it is not.

### How is Kuratowski’s theorem used in planarity testing?

The Fraysseixâ€“Rosenstiehl planarity criterion can be used directly as part of algorithms for planarity testing, while Kuratowski’s and Wagner’s theorems have indirect applications: if an algorithm can find a copy of K5 or K3,3 within a given graph, it can be sure that the input graph is not planar and return without additional computation.