par Aloupis, Greg 
;Ballinger, Brad;Collette, Sébastien ;Langerman, Stefan ;Pór, Attila;Wood, David
Référence Thirty Essays on Geometric Graph Theory, Springer New York, page (31-48)
Publication Publié, 2014-07
;Ballinger, Brad;Collette, Sébastien ;Langerman, Stefan ;Pór, Attila;Wood, David Référence Thirty Essays on Geometric Graph Theory, Springer New York, page (31-48)
Publication Publié, 2014-07
Partie d'ouvrage collectif
| Résumé : | This paper studies problems related to visibility among points in the plane. A point x blocks two points v and w if x is in the interior of the line segment vw¯. A set of points P is k-blocked if each point in P is assigned one of k colors, such that distinct points v, w ∈ P are assigned the same color if and only if some other point in P blocks v and w. The focus of this paper is the conjecture that each k-blocked set has bounded size (as a function of k). Results in the literature imply that every 2-blocked set has at most 3 points, and every 3-blocked set has at most 6 points. We prove that every 4-blocked set has at most 12 points, and that this bound is tight. In fact, we characterize all sets {n1,n2,n3,n4} such that some 4-blocked set has exactly n |
