https://en.wikipedia.org/wiki/Matching_(graph_theory)

Have you tried wiki?

0 votes

Perfect matching is a set of edges such that each vertex appears only once and all vertices appear at least once (EXACTLY one appearance). So for n vertices perfect matching will have n/2 edges and there won't be any perfect matching if n is odd.

I don't know whether i got it properly or not. Can please anybody explain the Perfect matching in a complete graph with simpler examples ?

I don't know whether i got it properly or not. Can please anybody explain the Perfect matching in a complete graph with simpler examples ?

2 votes

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching.

an **independent set** or **stable set** is a set of vertices in a graph, no two of which are adjacent.

A **maximum independent set** is an independent set of largest possible size for a given graph *G*. This size is called the **independence number** of *G*, and denoted *α*(*G*)

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Perfect matching exists for only graph with even number of vertices. No graph with odd number of vertices can contain perfect matching

here u get matching for complete graph

http://mathworld.wolfram.com/PerfectMatching.html

https://en.wikipedia.org/wiki/Independent_set_(graph_theory)

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in which every vertex of the graph is incident to exactly one edge of the matching.

Mam, I didn't understood,what u mean by above line. Can you please explain in a more simpler way first please :)