Erdős–Gallai Theorem

The Erdős–Gallai Theorem is a result in graph theory that helps us understand how many edges can connect a certain number of vertices while maintaining specific conditions. Specifically, it provides a criterion for determining whether a graph with a given number of vertices can have a certain number of edges without violating particular structural properties. In simpler terms, it outlines a way to check if a specific arrangement of connections among points (or nodes) is possible, which has implications in various fields like network design and social sciences where relationships between entities need to be analyzed.