Name
Abstract | ||
|---|---|---|
Consider a horizontal line in the plane and let @c(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 @c(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 @c(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. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.dam.2006.09.004 | Discrete Applied Mathematics |
Keywords | Field | DocType |
semi-order,multiplicative threshold,indifference graph,well-known order structure,interval order,numerical representation,n circle,new nontransitive preference structure,p iff,tangent circle graph,tangent circle preference structure,preference relation,decision theory,interval graph,asymmetric binary relation p,nontransitive preferences,semi-order structure,interval,representation,plan,binary relation,optimization,interpretation,binary relations,combinatorics,plane | Ford circle,Discrete mathematics,Combinatorics,Power of a point,Seven circles theorem,Tangent lines to circles,Circle packing theorem,Generalised circle,Osculating circle,Mathematics,Six circles theorem | Journal |
Volume | Issue | ISSN |
155 | 4 | Discrete Applied Mathematics |
Citations | PageRank | References |
2 | 0.43 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Moncef Abbas | 1 | 40 | 6.95 |
| Marc Pirlot | 2 | 333 | 39.10 |
| Philippe Vincke | 3 | 120 | 15.01 |