isBipartite -- determines if a graph is bipartite

Synopsis

Usage:
b = isBipartite G
Inputs:
- G, a graph
Outputs:
- b, a Boolean value, true if G is bipartite, false otherwise

Description

The function isBipartite determines if a given graph is bipartite. A graph is said to be bipartite if the vertices can be partitioned into two sets W and Y such that every edge has one vertex in W and the other in Y. Since a graph is bipartite if and only if its chromatic number is 2, we can check if a graph is bipartite by computing its chromatic number.

i1 : S = QQ[a..e];

i2 : t = graph {a*b,b*c,c*d,a*e} -- a tree (and thus, bipartite)

o2 = Graph{edges => {{a, b}, {b, c}, {c, d}, {a, e}}}
           ring => S
           vertices => {a, b, c, d, e}

o2 : Graph

i3 : c5 = cycle S -- 5-cycle (not bipartite)

o3 = Graph{edges => {{a, b}, {b, c}, {c, d}, {d, e}, {a, e}}}
           ring => S
           vertices => {a, b, c, d, e}

o3 : Graph

i4 : isBipartite t

o4 = true

i5 : isBipartite c5

o5 = false

Ways to use `isBipartite` :

isBipartite(Graph)

isBipartite -- determines if a graph is bipartite

Synopsis

Description

See also

Ways to use isBipartite :

Ways to use `isBipartite` :