Writing a program to check if a graph is bipartite

问题

I need to write a program that check if a graph is bipartite.

I have read through wikipedia articles about graph coloring and bipartite graph. These two article suggest methods to test bipartiteness like BFS search, but I cannot write a program implementing these methods.

回答1:

Why can't you? Your question makes it hard for someone to even write the program for you since you don't even mention a specific language...

The idea is to start by placing a random node into a FIFO queue (also here). Color it blue. Then repeat this while there are nodes still left in the queue: dequeue an element. Color its neighbors with a different color than the extracted element and insert (enqueue) each neighbour into the FIFO queue. For example, if you dequeue (extract) an element (node) colored red, color its neighbours blue. If you extract a blue node, color its neighbours red. If there are no coloring conflicts, the graph is bipartite. If you end up coloring a node with two different colors, than it's not bipartite.

Like @Moron said, what I described will only work for connected graphs. However, you can apply the same algorithm on each connected component to make it work for any graph.

回答2:

http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/GraphAlgor/breadthSearch.htm

Please read this web page, using breadth first search to check when you find a node has been visited, check the current cycle is odd or even.

A graph is bipartite if and only if it does not contain an odd cycle.

回答3:

The detailed implementation is as follows (C++ version):

struct NODE
{
    int color;
    vector<int> neigh_list;
};

bool checkAllNodesVisited(NODE *graph, int numNodes, int & index);

bool checkBigraph(NODE * graph, int numNodes)
{
    int start = 0;

    do 
    {
        queue<int> Myqueue;
        Myqueue.push(start);
        graph[start].color = 0;

        while(!Myqueue.empty())
        {
            int gid = Myqueue.front();
            for(int i=0; i<graph[gid].neigh_list.size(); i++)
            {
                int neighid = graph[gid].neigh_list[i];
                if(graph[neighid].color == -1)
                {
                    graph[neighid].color = (graph[gid].color+1)%2; // assign to another group
                    Myqueue.push(neighid);
                }
                else
                {
                    if(graph[neighid].color == graph[gid].color) // touble pair in the same group
                        return false;
                }
            }
            Myqueue.pop();
        }
    } while (!checkAllNodesVisited(graph, numNodes, start)); // make sure all nodes visited 
                                            // to be able to handle several separated graphs, IMPORTANT!!!

    return true;
}

bool checkAllNodesVisited(NODE *graph, int numNodes, int & index)
{
    for (int i=0; i<numNodes; i++)
    {
        if (graph[i].color == -1)
        {
            index = i;
            return false;
        }
    }

    return true;
}

来源：https://stackoverflow.com/questions/2889036/writing-a-program-to-check-if-a-graph-is-bipartite

标签

algorithm

graph

bipartite