The graph K3,3 is a complete bipartite graph consisting of two sets of three vertices each. In this graph, every vertex from one set is connected to every vertex in the other set, resulting in a total of nine edges. This structure is often used in graph theory to illustrate relationships between two distinct groups. K3,3 is notable for being non-planar, meaning it cannot be drawn on a flat surface without edges crossing. It serves as a fundamental example in the study of graph properties and is often referenced in discussions about Kurath's theorem and graph coloring.