Which algorithm is primarily used for finding the minimum spanning tree in a graph?

Kruskal's algorithm is specifically designed to find the minimum spanning tree of a connected, weighted graph. The algorithm operates by constructing the tree gradually, adding edges in order of increasing weight, while ensuring that no cycles are formed. This greedy approach guarantees that whenever an edge is added, it maintains the property of the minimum spanning tree, which is that it connects all vertices with the minimum possible total edge weight.

In contrast, dynamic programming is a broader technique used to solve optimization problems where a problem can be broken down into simpler subproblems. While it has applications in many areas, it is not specifically tailored for finding minimum spanning trees.

Depth-first search (DFS) is a traversal algorithm used to explore nodes and edges of a graph, but it doesn't provide a mechanism for finding a minimum spanning tree.

The Bellman-Ford algorithm is primarily used for finding the shortest path from a single source vertex to all other vertices in a graph, particularly in graphs that may contain negative weight edges. It is not focused on constructing spanning trees.

Thus, Kruskal's algorithm is the correct choice for finding minimum spanning trees due to its efficient and straightforward greedy approach.