I need help with this question.
Let G be a bipartite graph with bipartition $(A,B)$, such that $|A| = |B| = 10$, and every vertex of G has degree at least 5. Show that G has a perfect matching.
We are given the following hint : *Show that if X is a vertex cover of G then either $|X \cap A| \geq 5$ and $|X \cap B| \geq 5$, or $A \subseteq X$, or $B \subseteq X.$
This somehow relates to König's Theorem which states that in a bipartite graph G, the minimum size of a vertex cover in G is equal to the maximum size of a matching in G.