Rom Pinchasi

Department of Mathematics
 Technion  Israel Institute of Technology
 Haifa, Israel 32000
 room (you know what to put here) math.technion.ac.il
Current Interests:
Combinatorics, Discrete Geometry, Computational Geometry, Topological Graphs
Courses:
Topics in Combinatorics: 106928
A NEW!!! course on Math Puzzles: 104186
Selected Papers:
(Some links do not point to a file; please contact me by email if you
need a copy.)

R. Pinchasi,
GallaiSylvester Theorem for Pairwise Intersecting Unit Circles,
Discrete and Computational Geometry,
28 (2002), 607624.

P. Agarwal, E. Nevo, J. Pach, R. Pinchasi, M. Sharir, and S. Smorodinsky,
Lenses in Arrangements of Pseudocircles and their Applications,
J. ACM, {\bf 51}, (2004), 139186. Also in
ACM Symposium on Computational Geometry, June 2002,
Universitat Polit\'ecnica de Catalunya, Barcelona, Spain. 123132.

J. Pach, R. Pinchasi, G. Tardos, G. T\'oth,
Geometric Graphs with no SelfIntersecting Path of Length Three,
Graph Drawing 2002, Lecture Notes in Computer Science 2528,
SpringerVerlag, Berlin, 2002, 295311. Also in
European J. Combinatorics , {\bf 25} (2004), no. 6, 793811.

N. Alon, H. Last, R. Pinchasi, and M. Sharir,
On the Complexity of Arrangements of Circles in the Plane,
Discrete and Computational Geometry, {\bf 26} (2001), 465492.

J. Pach and R. Pinchasi,
On the Number of Balanced Lines,
Discrete and Computational Geometry, {\bf 25} (2001),
611628.

J. Pach and R. Pinchasi,
Bichromatic Lines With Few Points,
J. Combinatorial Theory Ser. A,
{\bf 90} (2000), 326335.

J. Pach and R. Pinchasi,
Unit Equilateral Triangles Induced by
Point Sets in Convex Position,
American Mathematical Monthly,
{\bf 110} (2003), 400406.

J. Pach, R. Pinchasi, and M. Sharir,
A Tight Bound for the Number of Different Directions
in Three Dimensions,
in 19th ACM Symposium on Computational Geometry,
San Diego, USA, 2003, pp 106113. Also in
J. Combinatorial Theory, ser. A. {\bf 108} (2004), 116.

R. Pinchasi and R. Radoi\v ci\'c,
On the Number of Edges in a Topological Graph with no
Selfintersecting Cycle of Length $4$,
appeared in 19th ACM Symposium on Computational Geometry,
San Diego, USA, 2003, pp 98103. Also to appear in
Towards a Theory of Geometric Graphs , 233243, Contemp. Math., 342,
Amer. Math. Soc. Providence, RI, 2004.(J. Pach Ed.).

R. Pinchasi,
Lines With Many Points On Both Sides,
Discrete and Computational Geometry, {\bf 30} (2003), 415435.

R. Pinchasi,
On the Size of a Radial Set,
Proc. Japan Conference on Discrete and Computational Geometry,
Lecture Notes in Computer Science (LNCS, SpringerVerlag),
2003, 233245.

M.A. Perles and R. Pinchasi,
Large Sets Must Have Either a $k$Edge or a $(k+2)$Edge,
Towards a Theory of Geometric Graphs, 225232, Contemp. Math., 342,
Amer. Math. Soc. Providence, RI, 2004. (J. Pach Ed.).

R. Pinchasi and M. Sharir,
On Graphs that Do not Contains the Cube and Related Problems,
Combinatorica, {\bf 25} (2005), no. 5, 615623.

J. Pach, R. Pinchasi, M. Sharir, and G. T\'oth,
Topological Graphs with no Large Grids,
Graphs and Combinatorics, {\bf 21} (2005), no. 3, 355364.

D.J. Kleitman and R. Pinchasi,
A Note on the Existence of a Directions Path,
Disc. and Comp. Geom. , {\bf 33} (2005), no. 2, 223229.

S. Onn and R. Pinchasi,
The Minimum Number of EdgeDirections of a Convex Polytope,
J. Combinatorial Theory, ser. A. {\bf 107}, (2004), no. 1, 147151.

N. Alon, J. Pach, R. Pinchasi, R. Radoi\v ci\'c, M. Sharir
Crossing Patterns of SemiAlgebraic Sets,
J. Combinatorial Theory, ser. A. {\bf 111} (2005), no. 2, 310326.

R. Pinchasi and S. Smorodinsky,
On The Delaunay Graph of a Geometric Graph,
proc. 20th ACM Symp. on Computational Geometry, (2004). 378382.

R. Pinchasi, R. Radoi\v ci\'c , and M. Sharir,
On Empty Convex Polygons in a Planar Point Set,
J. Combinatorial Theory, ser. A., {\bf 113} (2006), no. 3, 385419.
Also in proc. 20th ACM Symp. on Computational Geometry ,
(2004). 391400.

M.A. Perles and R. Pinchasi,
Forbidden $k$Sets in the Plane,
SIDMA , accepted.

J. Pach and R. Pinchasi,
A Long NonIntersecting Path Among Disjoint Segments in the Plane,
Combinatorial and computational geometry ,
495500, Math. Sci. Res. Inst.
Publ., {\bf 52}, Cambridge Univ. Press, Cambridge, 2005.

H. Last and R. Pinchasi>
At Least $n1$ Intersection Points Among $n$ Unit Circles
Disc. and Comp. Geom. accepted.

R. Pinchasi,
On the number of distinct directions of planes
determined by $n$ points in $\mathbb{R}^3$
submitted.

J. Pach, R. Pinchasi, and M. Sharir,
Solution of Scott's Problem on the Number of Directions
Determined by a Point Set in $3$Space
Discrete Comput. Geom. {\bf 38} (2007), 399441.

R. Pinchasi and G. Rote,
On the maximum size of an antichain of $k$sets and convex
pseudodiscs
submitted.

N. Alon, A. Pinchasi, and R. Pinchasi,
On Some Isoperimetric Inequality In The Universal Covering Space Of The
Punctured Plane
Discrete Mathematics, accepted.

A. Perlstein and R. Pinchasi,
Generalized Thrackles and Geometric Graphs in $\mathbb{R}^3$ with
no pair of Strongly Avoiding Edges
submitted.

N. Alon, T.H. Hall, C. Knauer, R. Pinchasi, R. Yuster
On Graphs and Algebraic Graphs
that do not Contain Cycles of Length $4$.
submitted.

R. Pinchasi,
The minimum number of distinct areas of triangles determined
by a set of $n$ points in the plane.
SIDMA , accepted.

E. Ackerman, K. Buchin, C. Knauer, R. Pinchasi, and G. Rote,
There are not too many Magic Configurations.
Discrete Comput. Geom. accepted.

R. Holzman, S. Lev, and R. Pinchasi,
Projecting difference sets on the positive orthant.
submitted.

R. Pinchasi,
Linear Algebra Approach to Geometric Graphs.
JCTA.

I. BenDan, R. Pinchasi, and R. Ziv,
Points with large $\alpha$depth.
submitted.

R. Pinchasi,
Geometric Graphs with no Two Parallel Edges.
Combinatorica, accepted.

S. Buzaglo, R. Pinchasi, and G. Rote,
Topological Hypergraphs.
submitted.

S. Buzaglo, R. Holzman, and R. Pinchasi,
On $k$intersecting curves and related problems.
submitted.

I. BenDan, R. Pinchasi, R. Ziv
On a problem of Felsner about quadrant depth..
submitted.

R. Apfelbaum, I. BenDan, S. Felsner, T. Miltzow, R. Pinchasi, T. Ueckerdt, R. Ziv,
Points with large quadrant depth.
submitted.

S. Lev, M. Muzychuk, R. Pinchasi,
Additive bases in abealian groups,
submitted.

I. Pak, R. Pinchasi,
How to cut out a convex polyhedron.
submitted. And a shorter version just of the main Lemma:
I. Pak, R. Pinchasi
Collapsing walls theorem.
American Mathematical Monthly, accepted.

R. Pinchasi,
Halving lines and measure concentration in the plane.
submitted.

E. Ackerman, R. Pinchasi, L. Scharf, M. Scherfenberg,
On inducing polygons and related problems.
submitted. And a shorter paper with the shorter proof only:
E. Ackerman, R. Pinchasi, L. Scharf, M. Scherfenberg,
Every simple arrangement of $n$ lines contains an inducing simple $n$gon.
submitted.

S. Kurz and R. Pinchasi,
Regular Matchstick Graphs.
American Mathematical Monthly , accepted.

R. Pinchasi and A. Pinkus,
Dominating Subsets under Projections.
SIAM J. Discrete Math. 24 (2010), no. 3, 910920.

E. Ackerman, T. Gelander, R. Pinchasi,
IceCreams and Wedge Graphs.
submitted.

E. Ackerman, N. Nitzan, R. Pinchasi,
The maximum number of edges in geometric graphs with pairwise
virtually avoiding edges.
submitted.

E. Ackerman and R. Pinchasi,
On the light side of geometric graphs.
submitted.

R. Pinchasi,
The Zone Theorem Revisited.
submitted.

E. Ackerman, J. Fox, R. Pinchasi,
A note on light geometric graphs.
submitted.

E. Ackerman, R. Pinchasi,
On the Degenerate Crossing Number.
submitted.

R. Pinchasi,
Points covered an odd number of times by translates.
submitted.

E. Ackerman, R. Pinchasi,
Covering a Chessboard with Staircase Walks.
submitted.

E. Ackerman, J. Pach, R. Pinchasi, R. Radoi\v ci\'c, G. T\'oth,
A note on coloring line arrangements.
submitted.

E. Ackerman, R. Pinchasi,
On coloring points with respected to rectangles.
submitted.

A. Ophir, R. Pinchasi,
Nearly Equal Distances in Metric Spaces.
submitted.

R. Pinchasi,
Extreme Intersection Points in Arrangements of Lines.
submitted.

R. Pinchasi,
A solution to a problem of Gr¨unbaum and Motzkin and of Erd˝os
and Purdy about bichromatic configurations of points in the plane.
Israel J. of Math., accepted.

R. Pinchasi,
Crossing by lines all edges of a line arrangement.
submitted.

G. Nivasch, J. Pach, R. Pinchasi, Sh. Zerbib,
The number of distinct distances from a vertex of a convex polygon.
submitted.

B. Aronov, M. Dulieu, R. Pinchasi, M. Sharir,
On the Union Complexity of Diametral Disks.
submitted.

A. Efrat, E. Ezra, R. Pinchasi, S. Sankararaman,
HittingSet Algorithms for Fast Data
Recovery in the Face of Geographic
Correlated Attacks.
submitted.

E. Ackerman, N. Nitzan, R. Pinchasi,
The maximum number of edges in geometric graphs with
pairwise virtually avoiding edges.
submitted.

V. F. Lev, R. Pinchasi,
Solving $a \pm b = 2c$
in the elements of finite sets.
submitted.

S. Gilboa, R. Pinchasi,
On the Union of Arithmetic Progressions.
submitted.

R. Pinchasi,
Crossing edges and faces of line arrangements in the plane.
submitted.

R. Pinchasi,
On the perimeter of $k$ pairwise disjoint convex bodies
contained in a convex set in the plane.
submitted.

R. Pinchasi,
A finite family of pseudodiscs must include a ``small''
pseudodisc.
submitted.

R. Pinchasi, G. Wolansky,
A generalization of Thue's theorem to packings of nonequal discs, and an
application to a discrete approximation of entropy.
submitted.
Unpublished manuscripts:
(These are preprints that are unpublished for some reason. We bring them here
in case one needs to refer to any of which.)

A link to the website of Avital Frumkin
Last update: August, 2014