Suppose a bipartite graph with two parts $A, B$, for every $b \in B$ we know $\deg(b) \ge 1$.
Prove there exists an adjacent $a \in A, b \in B$ such that $\frac{\deg(a)}{\deg(b)} \ge \frac{|B|}{|A|}$.
Existence of adjacent $a, b$ in a general bipartite graph (with a special degree condition) such that $\frac{\deg(a)}{\deg(b)} \ge \frac{|B|}{|A|}$
Nima Aryan
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