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

Published online by Cambridge University Press:  20 November 2018

T. S. Motzkin
University of California, Los Angeles
E. G. Straus
University of California, Los Angeles
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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 xi ≥ 0, Σxi = 1. What is

Research Article
Copyright © Canadian Mathematical Society 1965


1. MacDonald, J. E. Jr J Problem E1643, Amer. Math. Monthly, 70 (1963), 1099.Google Scholar
2. Turán, P., On the theory of graphs, Colloq. Math., 3 (1954), 1930.Google Scholar