Petersen's theorem

In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching. In other words, if a graph has exactly three edges at each vertex, and every edge belongs to a cycle, then it has a set of edges that touches every vertex exactly once.

Petersen's theorem

In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching. In other words, if a graph has exactly three edges at each vertex, and every edge belongs to a cycle, then it has a set of edges that touches every vertex exactly once.