Which of the following is not an application of inclusion-exclusion principle?ans.Maximum flow problemCounting intersectionsGraph coloringMatching of bipartite graphs Previous Marked for Review Next

The Inclusion-Exclusion Principle is a fundamental principle in combinatorics used for counting the number of elements in a union of sets. It is used to avoid double-counting elements that are in more than one set.

1. Maximum flow problem: This is a problem in network flow where the aim is to maximize the amount of flow that can be sent from a source to a sink in a flow network. This problem does not directly involve the counting of elements in a union of sets, so it is not an application of the Inclusion-Exclusion Principle.

2. Counting intersections: The Inclusion-Exclusion Principle is directly applicable here. It is used to count the total number of elements in a union of sets without double-counting elements that are in the intersection of these sets.

3. Graph coloring: This is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color. While this problem involves combinatorics, it does not directly involve the counting of elements in a union of sets, so it is not an application of the Inclusion-Exclusion Principle.

4. Matching of bipartite graphs: This is a problem of finding a maximum cardinality matching in a bipartite graph. While this problem involves combinatorics, it does not directly involve the counting of elements in a union of sets, so it is not an application of the Inclusion-Exclusion Principle.

So, the answer is that the Maximum flow problem, Graph coloring, and Matching of bipartite graphs are not applications of the Inclusion-Exclusion Principle.