When to Use Each Algorithm

Use Kuhn's algorithm for most problems: simple to code, works for $V \leq 1000$ in competitive programming. Use Hopcroft-Karp if you need $O(E \sqrt{V})$ for larger graphs ($V > 10^4$). Use max flow reduction if you already have a max flow implementation or the problem needs additional constraints (like edge capacities).

Use Hungarian algorithm for weighted matching where you want maximum total weight.