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# Maximum Bipartite Matching MCQ’s

_____________ is a matching with the largest number of edges.

a) Maximum bipartite matching

b) Non-bipartite matching

c) Stable marriage

d) Simplex

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Answer: a

Explanation: Maximum bipartite matching matches two elements with a property that no two edges share a vertex.

Maximum matching is also called as maximum cardinality matching.

a) True

b) False

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Answer: a

Explanation: Maximum matching is also called as maximum cardinality matching (i.e.) matching with the largest number of edges.

How many colours are used in a bipartite graph?

a) 1

b) 2

c) 3

d) 4

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Answer: b

Explanation: A bipartite graph is said to be two-colourable so that every edge has its vertices coloured in different colours.

What is the simplest method to prove that a graph is bipartite?

a) It has a cycle of an odd length

b) It does not have cycles

c) It does not have a cycle of an odd length

d) Both odd and even cycles are formed

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Answer: c

Explanation: It is not difficult to prove that a graph is bipartite if and only if it does not have a cycle of an odd length.

A matching that matches all the vertices of a graph is called?

a) Perfect matching

b) Cardinality matching

c) Good matching

d) Simplex matching

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Answer: a

Explanation: A matching that matches all the vertices of a graph is called perfect matching.

What is the length of an augmenting path?

a) Even

b) Odd

c) Depends on graph

d) 1

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Answer: b

Explanation: The length of an augmenting path in a bipartite graph is always said to be always odd.

In a bipartite graph G=(V,U,E), the matching of a free vertex in V to a free vertex in U is called?

a) Bipartite matching

b) Cardinality matching

c) Augmenting

d) Weight matching

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Answer: c

Explanation: A simple path from a free vertex in V to a free vertex in U whose edges alternate between edges not in M and edges in M is called a augmenting path.

A matching M is maximal if and only if there exists no augmenting path with respect to M.

a) True

b) False

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Answer: a

Explanation: According to the theorem discovered by the French mathematician Claude Berge, it means that the current matching is maximal if there is no augmenting path.

Which one of the following is an application for matching?

a) Proposal of marriage

b) Pairing boys and girls for a dance

c) Arranging elements in a set

d) Finding the shortest traversal path

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Answer: b

Explanation: Pairing boys and girls for a dance is a traditional example for matching. Proposal of marriage is an application of stable marriage problem.

Which is the correct technique for finding a maximum matching in a graph?

a) DFS traversal

b) BFS traversal

c) Shortest path traversal

d) Heap order traversal

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Answer: b

Explanation: The correct technique for finding a maximum matching in a bipartite graph is by using a Breadth First Search(BFS).

The problem of maximizing the sum of weights on edges connecting matched pairs of vertices is?

a) Maximum- mass matching

b) Maximum bipartite matching

c) Maximum weight matching

d) Maximum node matching

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Answer: c

Explanation: The problem is called as maximum weight matching which is similar to a bipartite matching. It is also called as assignment problem.

What is the total number of iterations used in a maximum- matching algorithm?

a) [n/2]

b) [n/3]

c) [n/2]+n

d) [n/2]+1

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Answer: d

Explanation: The total number of iterations cannot exceed [n/2]+1 where n=|V|+|U| denoting the number of vertices in the graph.

What is the efficiency of algorithm designed by Hopcroft and Karp?

a) O(n+m)

b) O(n(n+m)

c) O(√n(n+m))

d) O(n+2)

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Answer: c

Explanation: The efficiency of algorithm designed by Hopcroft and Karp is mathematically found to be O(√n(n+m)).

Who was the first person to solve the maximum matching problem?

a) Jack Edmonds

b) Hopcroft

c) Karp

d) Claude Berge

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Answer: a

Explanation: Jack Edmonds was the first person to solve the maximum matching problem in 1965.

From the given graph, how many vertices can be matched using maximum matching in bipartite graph algorithm?

a) 5

b) 4

c) 3

d) 2

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Answer: a

Explanation: One of the solutions of the matching problem is given by a-w,b-v,c-x,d-y,e-z. Hence the answer is 5.