Please help solve and explain & I will upvote!!!!

Ex.1 (BFS) In this exercise, I want you to recall BFS and briefly (but accurately) describe how to solve the following basic graph problems: 1. Given a connected undirected graph G=(V,E), check if it contains any cycle or not. 2. Given an undirected graph G=(V,E), check if it is bipartite or not. (A bipartite graph is a graph whose vertices can be divided into two disjoint sets U and V such that every edge connects a vertex in U to one in V.) 3. Prove the following statement: "A graph is bipartite if and only if it does not contain an odd cycle." Odd cycle is a cycle whose length is an odd number (e.g. a triangle is an odd cycle). To prove this you have to prove the two directions of the statement: First direction: if a graph is bipartite, then it does not contain an odd cycle. Second direction: if a graph does not contain an odd cycle, then the graph must be bipartite. Both of these directions should be relatively easy to prove