dfs.pf

def dfs(graph, start):
    color = {i : 'white' for i in graph}
    stack = [start]
    visited = []

    while stack:
        vertex = stack.pop()
        if color[vertex] == 'grey':
            return True
        color[vertex] = 'grey'
        visited.append(vertex)
        stack.extend((graph[vertex]))
        if  len(graph[vertex]) == 0:
            color[vertex] = 'black'
    return False

def cycle_exists(graph):
    for vertex in graph:
         if(dfs(graph, vertex)):
             return True
    return False


graph1 = { 0 : [],
           1 : [2,3],
           2 : [4],
           3 : [4],
           4 : [5],
           5 : [] }
assert(not cycle_exists(graph1))