Kőnig's Theorem

Kőnig's Theorem states that in a bipartite graph (a network divided into two groups with connections only between groups), the smallest number of connections needed to cover all nodes exactly once (a minimum vertex cover) is equal to the largest number of connections that can be paired without sharing any node (a maximum matching). Essentially, it links the maximum number of independent pairings between two sets to the minimum set of nodes that touches all connections, highlighting a balance between pairing possibilities and coverage requirements in such structured networks.