A matching or independent edge set in a graph is a set of edges without common vertices.
A perfect matching (also called 1-factor) is a matching which matches all vertices of the graph.
a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets and (that is, and are each independent sets) such that every edge connects a vertex in to one in.
Now imagine a bipartite graph like G which has a perfect matching.
Prove that there exists a vertex in G like V such that every edge connected to G is in a perfect matching.
Note : I tried to prove it but i have nothing to start with ! Thanks in advance.
Edit : The graph is a simple undirected graph and i don't know anything about "strongly" connected graphs.