Petersen (in relation to Petersen's theorem)

Petersen's theorem states that every regular graph with an even number of vertices can be decomposed into perfect matchings, meaning the edges can be split into pairs where each pair connects two vertices and covers all vertices without overlap. In particular, for a 3-regular graph (each vertex connected to three others), it can be divided into three such perfect matchings. This theorem is fundamental in graph theory because it guarantees the existence of these perfect pairings, which have applications in network design, scheduling, and matching problems.