I am working on a problem set for school right now and I have the following question:
Let $G$ be an arbitrary bipartite graph. What is the smallest possible girth of $G$? Explain
I have been thinking about this problem and I believe the answer is 2, because you could have a loop between two vertices $u,v$ where when $A$ and $B$ are bipartitions of a bipartite graph $G$ you have $u\in A$ and $v\in B$. I guess my question is: are loops possible in a bipartite graph? I think they are but we have spent so much time on simple graphs this semester I just want to make sure. Any help would be greatly appreciated.