Barany, ImrePach, Janos2014-01-092014-01-092014-01-09201410.1016/j.jctb.2013.10.001https://infoscience.epfl.ch/handle/20.500.14299/99157WOS:000328235500005Given d + 1 hyperplanes h(1),..., h(d+1) in general position in R-d, let Delta(h(1),..., h(d+1)) denote the unique bounded simplex enclosed by them. There exists a constant c(d) > 0 such that for any finite families H-1,..., Hd+1 of hyperplanes in R-d, there are subfamilies H-i* subset of H-i with vertical bar H-i*vertical bar >= c(d)vertical bar H-i vertical bar and a point p is an element of R-d with the property that p is an element of Delta(h(1),..., h(d+1)) for all h(i) is an element of H-i*. (C) 2013 Elsevier Inc. All rights reserved.HyperplanesHypergraphsIntersecting simplicestext::journal::journal article::research article