Before proof, we will define some basic terminologies.

**Bipartite Graph:** A graph whose vertices can be divided into 2 disjoint sets such that no two vertices in the same set are adjacent to each other is called Bipartite Graph.

**Proof**

We can prove the given statement by contradiction. Suppose you have a bipartite graph G. Let V1 and V2 be the bipartitions of G.

Suppose there is a triangle in the graph. The triangle is shown below:-

Since the graph is bipartite, we should be able to divide vertices – a, b, and c in set V1, V2 such that no two vertices are adjacent to each other. But this is not possible. We cannot separate a, b, c without atleast 2 of them being in the same set.

For example, put vertex a in V1 and vertex b in V2. Now if we put vertex c in V1 or V2, it will violate bipartite property since c is adjacent to both a and b. Therefore, graph G cannot be bipartite.

Therefore, our assumption that a bipartite graph contains a triangle is incorrect. Thus, we can say that a graph that contains a triangle cannot be bipartite.

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