A graph is said to be bipartite if all its vertices can be partitioned into two
ID: 3542976 • Letter: A
Question
A graph is said to be bipartite if all its vertices can be partitioned into two
disjoint subsetsX and Y so that every edge connects a vertex inX with a vertex
in Y . (One can also say that a graph is bipartite if its vertices can be colored in
two colors so that every edge has its vertices colored in different colors; such
graphs are also called 2-colorable.) For example, graph (i) is bipartite while
graph (ii) is not.
(i)
x1-y1-x3
| | |
y2-x2-y3
(ii)
a-b
| / |
c-d
a. Design a DFS-based algorithm for checking whether a graph is bipartite.
b. Design a BFS-based algorithm for checking whether a graph is bipartite.
Explanation / Answer
a.DFS-based
b.BFS-based
1. Assign RED color to the source vertex (putting into set U).
2. Color all the neighbors with BLUE color (putting into set V).
3. Color all neighbor