Kurath's theorem is a result in the field of graph theory, specifically concerning the properties of certain types of graphs known as perfect graphs. The theorem states that if a graph is perfect, then its chromatic number equals the size of the largest clique in the graph. This means that the minimum number of colors needed to color the graph's vertices, so that no two adjacent vertices share the same color, is directly related to the largest complete subgraph within it. The theorem is significant because it provides a clear criterion for identifying perfect graphs. It also connects various concepts in graph theory, such as cliques, coloring, and complement graphs, enhancing our understanding of how these elements interact within a graph's structure.