par Abbas, Moncef;Pirlot, Marc ;Vincke, Philippe
Référence Discrete applied mathematics, 155, 4, page (429-441)
Publication Publié, 2007-02
Article révisé par les pairs
Résumé : Consider a horizontal line in the plane and let γ (A) be a collection of n circles, possibly of different sizes all tangent to the line on the same side. We define the tangent circle graph associated to γ (A) as the intersection graph of the circles. We also define an irreflexive and asymmetric binary relation P on A; the pair (a, b) representing two circles of γ (A) is in P iff the circle associated to a lies to the right of the circle associated to b and does not intersect it. This defines a new nontransitive preference structure that generalizes the semi-order structure. We study its properties and relationships with other well-known order structures, provide a numerical representation and establish a sufficient condition implying that P is transitive. The tangent circle preference structure offers a geometric interpretation of a model of preference relations defined by means of a numerical representation with multiplicative threshold; this representation has appeared in several recently published papers. © 2006 Elsevier B.V. All rights reserved.