… sets are scaled copies of a convex polygon. We also … convex transversal of a maximum
number of pairwise-disjoint segments (or convex polygons) in 2D if the vertices of the transversal …

… convex sets have a line transversal then this transversal meets the sets in a specific order
(if we take the line to be directed). Thus, if the family A = {al, ... ,an} is met by a directed line, …

… Clearly, if F has a ρ-transversal plane, then F has a topological ρ-transversal of index (m,
k), … convex sets in Rd a topological ρ-transversal of index (m, k) implies an ordinary ρ-transversal…

… Much research on geometric transversals … transversals to a family A of convex sets. This
research includes conditions on the existence of transversals to special families of convex sets, …

… transversals—a brief background. In this paper we study the combinatorial complexity of the
set of line transversals of a collection of convex … of line transversals to a collection of convex …

… convex compact set K in R2 in which any two sets have a nonempty intersection there exists
a 3-transversal… the order of a transversal for a family of translates of a convex compact set in …

… A common transversal for a disjoint family si of η convex sets intersects the members of A in
a definite order, up to reversal, and therefore determines a permutation ρ of si and its reversal…

… to the family \(\mathcal {F}\), we say that T is a k-flat transversal. For example, a line transversal
is a line that intersects every member of \(\mathcal {F}\) and a hyperplane transversal is a …

… A transversal is called convex if it is a convex set. Our interest in convex transversals is
partly motivated by the paper [6], whose main geometric ingredient is the assertion that the …

… space of line transversals to pairwise disjoint convex sets in \(\mathbb {R}^3\), and we
extend a theorem of Karasev and Montejano regarding colorful intersections and k-transversals. …