Problem 4 One of the uses of Breadth-First Search is to determine whether a grap

Question

Problem 4

One of the uses of Breadth-First Search is to determine whether a graph is bipartite, i.e., its vertices V can be split into exactly two disjoint sets V1 , V2 such that every edge in the graph connects a vertex in V1 to a vertex in V2.

The “test for bipartiteness” starts off as follows: we run the BFS algorithm starting from some node s and color s blue. Then we color of all s’s neighbors red, the next layer of neighbors blue, and so on. Once this BFS algorithm is complete, how can you tell if the given graph is bipartite or not? Pseudocode is not necessary for this problem, just an English-language explanation.

Explanation / Answer

The test for Bipartiteness is a check performed on a graph to determine whether its vertices can be divided into two disjoint sets and (that is, and are each independent sets) such that every edge connects a vertex in to one in.In other words, A Bipartite Graph is a graph whose vertices can be divided into two independent sets, U and V such that every edge (u, v) either connects a vertex from U to V or a vertex from V to U.

Condition - A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color.

For this, we use BFS algorithm which works in following manner -

Kindly rate my answer.ThankYou.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.