turan_graph

turan_graph(n, r)

Return the Turan Graph

The Turan Graph is a complete multipartite graph on n vertices with r disjoint subsets. It is the graph with the edges for any graph with n vertices and r disjoint subsets.

Given n and r, we generate a complete multipartite graph with \(r-(n \mod r)\) partitions of size \(n/r\), rounded down, and \(n \mod r\) partitions of size \(n/r+1\), rounded down.

Parameters:

• n (int) – The number of vertices.
• r (int) – The number of partitions. Must be less than or equal to n.

Notes

Must satisfy \(1 <= r <= n\). The graph has \((r-1)(n^2)/(2r)\) edges, rounded down.