5 papers · 1 filter
On the -dimensional algebraic connectivity of graphs
Alan Lew, Eran Nevo, Yuval Peled +1
The -dimensional algebraic connectivity of a graph , introduced by Jordán and Tanigawa, is a quantitative measure of the -dimensional rigidity of that i…
On rich lenses in planar arrangements of circles and related problems
Esther Ezra, Orit E. Raz, Micha Sharir +1
We show that the maximum number of pairwise non-overlapping -rich lenses (lenses formed by at least circles) in an arrangement of circles in the plane is $O\left(\frac{n…
Dense graphs have rigid parts
Orit E. Raz, József Solymosi
While the problem of determining whether an embedding of a graph in is {\it infinitesimally rigid} is well understood, specifying whether a given embedding of $G…
Expanding polynomials: A generalization of the Elekes-Rónyai theorem to variables
Orit E. Raz, Zvi Shem Tov
We prove the following statement. Let , for some , and assume that depends non-trivially in each of . Then one of the fo…
On the number of unit-area triangles spanned by convex grids in the plane
Orit E. Raz, Micha Sharir, Ilya D. Shkredov
A finite set of real numbers is called convex if the differences between consecutive elements form a strictly increasing sequence. We show that, for any pair of convex sets $A, B\s…