Fairbairn's Theorem is a result in the field of mathematics, specifically in the area of graph theory. It states that in any finite graph, if a certain condition regarding the edges and vertices is met, then it is possible to find a specific type of subgraph that satisfies particular properties. This theorem helps in understanding the structure and behavior of graphs. The theorem is named after William Fairbairn, who contributed to the study of graph properties. Fairbairn's Theorem has applications in various fields, including computer science, network design, and optimization, where understanding relationships within data is crucial.