answer (b) and (c) please and use BFS

A bipartite graph is a graph G = (V, E) whose vertices can be partitioned into two sets (V = VUV2 and Vin V2 = 0) such that there are no edges between vertices in the same set (for instance, if U, V E V1, then there is no edge between u and v). = u (a) Give a linear-time algorithm to determine whether an undirected graph is bipartite. (b) There are many other ways to formulate this property. For instance, an undirected graph is bipartite if and only if it can be colored with just two colors. Prove the following formulation: an undirected graph is bipartite if and only if it contains no cycles of odd length. (c) At most how many colors are needed to color in an undirected graph with exactly one odd- length cycle