Strong isometric dimension, biclique coverings, and Sperner’s Theorem Dalibor Fronˇ cek ∗ Department of Mathematics and Statistics University of Minnesota Duluth 1117 University Drive, Duluth, MN 55812, U.S.A. dfroncek@d.umn.edu Janja Jerebic Department of Mathematics and Computer Science PeF, University of Maribor Koroˇ ska cesta 160, 2000 Maribor, Slovenia janja.jerebic@uni-mb.si Sandi Klavˇ zar † Department of Mathematics and Computer Science PeF, University of Maribor Koroˇ ska cesta 160, 2000 Maribor, Slovenia sandi.klavzar@uni-mb.si PetrKov´aˇ r Department of Mathematics and Descriptive Geometry Technical University of Ostrava 17. listopadu 15, 708 33 Ostrava – Poruba, Czech Republic petr.kovar@vsb.cz Abstract The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner’s Theorem, the strong isometric dimension of the Hamming graphs K 2 K n is determined. Keywords: strong isometric dimension; biclique covering; Sperner’s Theorem AMS subject classification (2000): 05C12, 05C70, 05D05 ∗ Supported by the University of Minnesota Duluth Grant Grant 177–1009. † Supported by the Ministry of Education, Science and Sport of Slovenia under the grant P1- 0297. 1