Documentation

This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

`Graph`::`bipartite`

Finds out if a graph is bipartite.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

Syntax

```Graph::bipartite(`G`, <`Bool | Lists`>)
```

Description

`Graph::bipartite(G)` finds out whether G is bipartite or not.

`Graph::bipartite(G, Sets)`: If G is bipartite, then a list containing two lists will be returned. Each of the lists contains the vertices belonging to the set. If G is not bipartite, then `FAIL` will be returned instead of any list.

`Graph::bipartite(G, Bool)` offers the same result as `Graph::bipartite(G)`. If G is bipartite, then `TRUE` will be returned, otherwise `FALSE`.

Examples

Example 1

A small graph containing 3 vertices with 2 edges connecting them is created:

```G := Graph([a, b, c], [[a, b], [b, c]]): Graph::bipartite(G, Lists); Graph::bipartite(G, Bool)```

Two lists with vertices are shown. Another word for bipartite is two-colorable. This means that the graph above can be colored with only two colors so that no two vertices have the same color if connected with an edge. The bottom output could also be accomplished without using the parameter `Bool`:

`Graph::bipartite(G)`

The following example shows what happens when a graph is not bipartite (an edge is added to connect the vertices a and c):

```G2 := Graph::addEdges(G, [[a, c]]): Graph::bipartite(G2, Lists); Graph::bipartite(G2, Bool)```

Parameters

 `G` `Graph`

Options

 `Lists` If Lists is stated the return value will be a list of two lists containing the (sorted) vertices belonging to each set, or `FAIL`. `Bool` If Bool is stated the return value will be either `TRUE` or `FALSE`. This is the default.

Return Values

Depending on the options either a boolean value or list-sets will be returned.