Kuratowski's Theorem

Kuratowski's Theorem is a principle in topology that deals with how certain shapes, known as planar graphs, can be represented on a flat surface without any edges crossing. The theorem states that a graph is planar if it can be drawn in two dimensions without overlaps, and it identifies specific configurations called K5 (a complete graph of five vertices) and K3,3 (a bipartite graph with three vertices on each side) as the only forbidden shapes that ensure a graph cannot be drawn this way. Essentially, it helps us understand the limits of drawing complex connections neatly on a page.