Linear Inequalities among Graph Invariants: using GraPHedron to uncover optimal relationships Julie Christophe Universit´ e Libre de Bruxelles, Belgium Sophie Dewez Universit´ e Libre de Bruxelles, Belgium Jean-Paul Doignon 1 Universit´ e Libre de Bruxelles, Belgium Sourour Elloumi CEDRIC, Conservatoire National des Arts et M´ etiers, Paris, France Gilles Fasbender Universit´ e Libre de Bruxelles, Belgium Philippe Gr´ egoire Universit´ e Libre de Bruxelles, Belgium David Huygens Universit´ e Libre de Bruxelles, Belgium Martine Labb´ e Universit´ e Libre de Bruxelles, Belgium Hadrien M´ elot Universit´ e de Mons-Hainaut, Belgium Hande Yaman Department of Industrial Engineering, Bilkent University, Turkey 1 Correspondence to: J.-P. Doignon, U.L.B. c.p. 216, Bd du Triomphe, 1050 Bruxelles, Belgium. E-mail: doignon@ulb.ac.be. Research supported by “Communaut´ efran¸caise de Belgique - Actions de Recherche Concert´ ees”. Version: February, 1, 2008. 1