双向图

Question

How do you find out whether an undirected graph is Biconnected or not using its depth first search traversal. Is there any other way than traversing the whole graph to find disconnected pieces of the graph.

Answer 1

You calculate the low(v) for every vertex in linear time (ie during the execution of the DFS). And there exists a bridge (ie an edge whose removal will disconnect the graph ==> not biconnected) iff there's a non-root vertex whose low value is itself OR if the root has more than one child.

It's explained here on point 5.2 http://www.cse.ohio-state.edu/~lai/780/graph.pdf

Answer 2

我对此没有任何答案，但是我的直觉认为您将必须进行深度优先搜索遍历，因为图的biconnected属性是整个图的属性，而不是图的任何子集。