Petersen–Morley theorem

The Petersen–Morley theorem is a result in graph theory that concerns the structure of certain types of graphs. It states that for every sufficiently large graph, if it contains no complete subgraph \( K_n \) of size \( n \), then the graph can be colored with \( n-1 \) colors such that no two adjacent vertices share the same color. The theorem is particularly relevant when discussing the properties of planar graphs and colorability.