Question

Let G be a bipartite graph with bipartition (A, B) where |A| = |B| = 2k for some positive integer k. Suppose that |N(X)| ≥ |X| for all X ⊆ A with |X| ≤ k, and |N(Y)| ≥ |Y| for all Y ⊆ B with |Y | ≤ k. Prove that G has a perfect matching.

Name: let g be a bipartite graph with bipartition a b where a b 2k for some positive integer k suppose that nx x for all x a with x k and ny y for all y b with y k prove that g has a perfect match 76292
Uploaded: 2022-11-05T10:15:26-08:00
Duration: 2 min 4 s
Channel: Sri K
Description: let g be a bipartite graph with bipartition a b where a b 2k for some positive integer k suppose that nx x for all x a with x k and ny y for all y b with y k prove that g has a perfect match 76292

          Let G be a bipartite graph with bipartition (A, B)
where |A| = |B| = 2k for some positive
integer k. Suppose that |N(X)| ≥ |X| for
all X ⊆ A with |X| ≤ k,
and |N(Y)| ≥ |Y| for
all Y ⊆ B with |Y | ≤ k. Prove
that G has a perfect matching.

Added by Jason M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

11/05/2022

Step 1

Step 1: Since G is a bipartite graph with bipartition (A, B) where |A| = |B| = 2k, we know that G has 2k vertices in each part. Show more…

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Let G be a bipartite graph with bipartition (A, B) where |A| = |B| = 2k for some positive integer k. Suppose that |N(X)| ≥ |X| for all X ⊆ A with |X| ≤ k, and |N(Y)| ≥ |Y| for all Y ⊆ B with |Y | ≤ k. Prove that G has a perfect matching.