Perfect matching in a tree

Question

I came across a definition of Perfect matching: a set of edges that touches each node exactly once.

However, i didnt really understand the definition. Can somebody give me an example of any such edge. Or may be point me towards some reference that does.

I tried to google but it didnt give me any example.

Answer 1

A perfect matching set is any set of edges in a graph where every vertex in the graph is touched by exactly one edge in the matching set. If you consider a graph with 4 vertices connected so that the graph resembles a square, there are two perfect matching sets, which are the pairs of parallel edges. Since all the vertices are touched exactly once by either pair. If you think about a graph with 3 vertices connected like a triangle, there is no perfect matching set, because if you take any pair of edges, one vertex is touched twice, but a single edge will always miss a vertex.

http://en.wikipedia.org/wiki/Perfect_matching

Your question mentions a tree, but a tree is just a special type of graph, so it still works the same.