Is Graph Bipartite?

Given an undirected graph, return true if and only if it is bipartite.

Recall that a graph is bipartite if we can split it’s set of nodes into two independent subsets A and B such that every edge in the graph has one node in A and another node in B.

The graph is given in the following form: graph[i] is a list of indexes j for which the edge between nodes i and j exists.  Each node is an integer between 0 and graph.length - 1.  There are no self edges or parallel edges: graph[i] does not contain i, and it doesn’t contain any element twice.

Example 1:
Input: [[1,3], [0,2], [1,3], [0,2]]
Output: true
The graph looks like this:
|    |
|    |
We can divide the vertices into two groups: {0, 2} and {1, 3}.
Example 2:
Input: [[1,2,3], [0,2], [0,1,3], [0,2]]
Output: false
The graph looks like this:
| \  |
|  \ |
We cannot find a way to divide the set of nodes into two independent subsets.


  • graph will have length in range [1, 100].
  • graph[i] will contain integers in range [0, graph.length - 1].
  • graph[i] will not contain i or duplicate values.
  • The graph is undirected: if any element j is in graph[i], then i will be in graph[j].
class Solution:
    def isBipartite(self, graph: List[List[int]]) -> bool:
        color = collections.defaultdict(lambda: -1)
        def dfs(v, cur_color):
            if color[v] != -1: return color[v] == cur_color
            color[v] = cur_color
            return all(dfs(e, cur_color ^ 1) for e in graph[v])
        return all(dfs(v, 0) for v in range(len(graph)) if color[v] == -1)

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