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IsBipartite

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsBipartite(G)

IsBipartite(G, P)

Parameters

G

-

graph

P

-

(optional) name

Description

• 

IsBipartite returns true if the graph G is bipartite and false otherwise. If a variable name P is specified, then this name is assigned a bipartition of the vertices as a list of lists.

• 

A graph G is bipartite if its set of vertices can be partitioned into two sets, V1 and V2, such that every edge in G connects a vertex in V1 or V2 to a vertex in the other set.

Examples

withGraphTheory:

K32CompleteGraph3,2

K32Graph 1: an undirected unweighted graph with 5 vertices and 6 edge(s)

(1)

IsBipartiteK32,bp

true

(2)

bp

1,2,3,4,5

(3)

DrawGraphK32,style=bipartite

AdjacencyMatrixK32

0001100011000111110011100

(4)

GCycleGraph5

GGraph 2: an undirected unweighted graph with 5 vertices and 5 edge(s)

(5)

IsBipartiteG

false

(6)

See Also

AdjacencyMatrix

BipartiteMatching

DrawGraph

RandomGraphs[RandomBipartiteGraph]