This question is from the subject Discrete Mathematics 2, where it involves basic set theory, combinatorics, graph theory etc. 5. Let G = (V, E) be a simple undirected graph. A perfect matching of G is a spanningsubgraph H such that the edges in H have pairwise empty intersection. For example, belowon the left is K4 and below on the right are the 3 perfect matchings of K4.AKA(a) Find a perfect matching in the graph below.(b) If G = (V, E) has a perfect matching, show that |V| is even.(c) Find a perfect matching of K6. How many perfect matchings are there of K6?(d) For n > 1, let F(n) be the number of perfect matchings of K2n, the complete graph on2n vertices. Find a recurrence relation for F(n).

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Description: This question is from the subject Discrete Mathematics 2, where it involves basic set theory, combinatorics, graph theory etc. 5. Let G = (V, E) be a simple undirected graph. A perfect matching of G is a spanningsubgraph H such that the edges in H ha

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(a) Find a perfect matching in the graph below. (b) If G = (V, E) has a perfect matching, show that |V| is even. (c) Find a perfect matching of K6. How many perfect matchings are there of K6?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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This question is from the subject Discrete Mathematics 2, where it involves basic set theory, combinatorics, graph theory etc.

5. Let G = (V, E) be a simple undirected graph. A perfect matching of G is a spanning
subgraph H such that the edges in H have pairwise empty intersection. For example, below
on the left is K4 and below on the right are the 3 perfect matchings of K4.
AKA
(a) Find a perfect matching in the graph below.
(b) If G = (V, E) has a perfect matching, show that |V| is even.
(c) Find a perfect matching of K6. How many perfect matchings are there of K6?
(d) For n > 1, let F(n) be the number of perfect matchings of K2n, the complete graph on
2n vertices. Find a recurrence relation for F(n).

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