Leetcode 886: Possible Bipartition

We want to split a group of n people (labeled from 1 to n) into two groups of any size. Each person may dislike some other people, and they should not go into the same group.

Given the integer n and the array dislikes where dislikes[i] = [ai, bi] indicates that the person labeled ai does not like the person labeled bi, return true if it is possible to split everyone into two groups in this way.

This problem can be solved by 2-coloring, that is recursively coloring node and its neighbor until it cannot be done.

def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:         
    graph = defaultdict(list)         
    colors = [0]*(n + 1)         
    for x,y in dislikes:             
        graph[x].append(y)             
        graph[y].append(x) 
         
    def dfs(curr,c):                         
        colors[curr] = c             
        for n in graph[curr]:                 
            if colors[n] == c:                     
                return False                 
            if colors[n] == 0 and not dfs(n,-c): 
                return False             
        return True 
         
    for g in graph:             
        if colors[g] == 0 and not dfs(g, 1):                 
            return False         
    return True  
# time complexity : O(V^2) ? 
# sapce complexity : O(V) ?