Maxima for Graphs and a New Proof of a Theorem of Turán

Abstract

Maximum of a square-free quadratic form on a simplex. The following question was suggested by a problem of J. E. MacDonald Jr. (1):Given a graph G with vertices 1, 2, . . . , n. Let S be the simplex in Eⁿ given by x_i ≥ 0, Σx_i = 1. What is