def eulerPath(graph):
        # counting the number of vertices with odd degree
        odd = [ x for x in graph.keys() if len(graph[x])&1 ]
        print odd
        odd.append( graph.keys()[0] )
    
    
        if len(odd)>3:
            return None
    
        stack = [ odd[0] ]
        path = []
    
        # main algorithm
        while stack:
            v = stack[-1]
            if graph[v]:
                u = graph[v][0]
                stack.append(u)
                # deleting edge u-v
                #print graph[u][ graph[u].index(v) ]
                #print graph[u].index(v)
                del graph[u][ graph[u].index(v) ]
                del graph[v][0]
            else:
                path.append( stack.pop() )
    
        return path
    
    stack_ = eulerPath({ 1:[2,3], 2:[1,3,4,5], 3:[1,2,4,5], 4:[2,3,5], 5:[2,3,4] })
    print stack_