Kruskal's theorem

Kruskal’s theorem states that, in certain mathematical settings involving trees labeled with data, the way these trees are organized is uniquely determined by their structure and labels, regardless of how you might rearrange or analyze parts of them. Essentially, it ensures a consistent, unambiguous way to identify and compare hierarchical data structures, which is crucial in fields like probability, combinatorics, and computer science for understanding complex, tree-like systems. The theorem guarantees that these labeled trees encode information in a distinct and reliable manner, allowing mathematicians to work with them confidently.