Question

A bipartite graph is a simple graph of which the vertices are decomposed into two disjoint sets such
that no two graph vertices within the same set are adjacent

Show that if every component of a graph is bipartite, then the graph is bipartite.

Answer 1

we know that A bipartite graph is a simple graph of which the vertices are decomposed into two disjoint sets such
that no two graph vertices within the same set are adjacent

let every component of of a graph is bipartite.

if the components are divided into sets A_{​​​​​​1} and B_{​​​​​​1}, A₂ and B​​​​_{​​​​​​2} then let
A = ∪_iA_i and B = ∪_iB_i
we can easily see that graph is bipartite because here we can decompose vertices into two disjoint sets .

hence graph is bipartite .

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