5. 6. Given an undirected graph with n vertices and m edges, find an O(n+m) time algorithm that determines whether it is possible to color all the vertices red and blue such that every edge is between a red vertex and blue vertex. If such a coloring exists, your algorithm should produce one. Give an algorithm that determines whether or not a given undirected graph contains a cycle. Your algorithm should run in time O(n) and independent of m.

5. 6. Given an undirected graph with n vertices and m edges, find an O(n+m) time algorithm that determines whether it is possible to color all the vertices red and blue such that every edge is between a red vertex and blue vertex. If such a coloring exists, your algorithm should produce one. Give an algorithm that determines whether or not a given undirected graph contains a cycle. Your algorithm should run in time O(n) and independent of m.