Complexity of the Euclidean max cut problem

We consider the following problem: given a complete edge-weighted undirected graph whose vertices are points of a $q$-dimensional space, find a cut of maximum total weight. Two special cases are analyzed where the edge weights are equal to (i) the Euclidean distances between points representing the vertices, (ii) the squares of these distances. We prove that both cases of the problem are strongly NP-hard do no permit FPTAS unless $\mathrm{P\neq NP}$. Bibliogr. 17.