Let $G$ be a bipartite graph in which the greatest degree of a vertex is 2019. Let $m$ be the least natural number for which we can color the edges of $G$ in $m$ colors so that each two edges with a common vertex from $G$ are in different colors. Show that $m$ doesn’t depend on $G$ and find its value.
1. **Understanding the Problem:**
   We are given a bipartite graph \( G \) where the maximum degree of any vertex is 2019. We need to find the minimum number of colors \( m \) required to color the edges of \( G \) such that no two edges sharing a common vertex have the same color.

2. **Applying König's Theorem:**
   König's theorem states that every bipartite graph with maximum degree \(\Delta\) can be edge-colored using exactly \(\Delta\) colors. This theorem is fundamental in graph theory and can be found in standard references such as R. Diestel's "Graph Theory".

3. **Maximum Degree Analysis:**
   In our problem, the maximum degree \(\Delta\) of the graph \( G \) is given as 2019. According to König's theorem, the number of colors required to edge-color the graph \( G \) is exactly \(\Delta\).

4. **Conclusion:**
   Since the maximum degree \(\Delta\) is 2019, the minimum number of colors \( m \) required to edge-color the graph \( G \) is 2019. This result is independent of the specific structure of the bipartite graph \( G \) and depends solely on the maximum degree.

\[
m = \Delta = 2019
\]

\(\blacksquare\)

The final answer is \( \boxed{ 2019 } \)