# homepage of Rom Pinchasi

# Rom Pinchasi

Technion - Israel Institute of Technology

Haifa, Israel 32000

E-mail: rom.pinchasi@gmail.com

IMPORTANT: Due to security issues, I may not be able to read messages that were sent to my Technion e-mail address after February 2023.

Please use my Gmail address for future communication.

### Current Interests:

Combinatorics, Discrete Geometry, Computational Geometry, Topological Graphs

### Courses:

Topics in Combinatorics: 106928

### Selected Papers:

(Some links do not point to a file; please contact me by email if you need a copy.)

R. Pinchasi, Gallai-Sylvester Theorem for Pairwise Intersecting Unit Circles, Discrete and Computational Geometry, 28 (2002), 607--624.

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), 139--186. Also in ACM Symposium on Computational Geometry, June 2002, Universitat Polit\'ecnica de Catalunya, Barcelona, Spain. 123--132.

J. Pach, R. Pinchasi, G. Tardos, G. T\'oth, Geometric Graphs with no Self-Intersecting Path of Length Three, Graph Drawing 2002, Lecture Notes in Computer Science 2528, Springer-Verlag, Berlin, 2002, 295--311. Also in European J. Combinatorics , {\bf 25} (2004), no. 6, 793--811.

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), 465-492.

J. Pach and R. Pinchasi, On the Number of Balanced Lines, Discrete and Computational Geometry, {\bf 25} (2001), 611--628.

J. Pach and R. Pinchasi, Bichromatic Lines With Few Points, J. Combinatorial Theory Ser. A, {\bf 90} (2000), 326--335.

J. Pach and R. Pinchasi, Unit Equilateral Triangles Induced by Point Sets in Convex Position, American Mathematical Monthly, {\bf 110} (2003), 400--406.

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 106--113. Also in J. Combinatorial Theory, ser. A. {\bf 108} (2004), 1--16.

R. Pinchasi and R. Radoi\v ci\'c, On the Number of Edges in a Topological Graph with no Self-intersecting Cycle of Length $4$, appeared in 19th ACM Symposium on Computational Geometry, San Diego, USA, 2003, pp 98--103. Also to appear in Towards a Theory of Geometric Graphs , 233--243, 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), 415--435.

R. Pinchasi, On the Size of a Radial Set, Proc. Japan Conference on Discrete and Computational Geometry, Lecture Notes in Computer Science (LNCS, Springer-Verlag), 2003, 233--245.

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, 225--232, 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, 615--623.

J. Pach, R. Pinchasi, M. Sharir, and G. T\'oth, Topological Graphs with no Large Grids, Graphs and Combinatorics, {\bf 21} (2005), no. 3, 355--364.

D.J. Kleitman and R. Pinchasi, A Note on the Existence of a Directions Path, Disc. and Comp. Geom. , {\bf 33} (2005), no. 2, 223--229.

S. Onn and R. Pinchasi, The Minimum Number of Edge-Directions of a Convex Polytope, J. Combinatorial Theory, ser. A. {\bf 107}, (2004), no. 1, 147--151.

N. Alon, J. Pach, R. Pinchasi, R. Radoi\v ci\'c, M. Sharir Crossing Patterns of Semi-Algebraic Sets, J. Combinatorial Theory, ser. A. {\bf 111} (2005), no. 2, 310--326.

R. Pinchasi and S. Smorodinsky, On The Delaunay Graph of a Geometric Graph, proc. 20th ACM Symp. on Computational Geometry, (2004). 378--382.

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, 385--419. Also in proc. 20th ACM Symp. on Computational Geometry , (2004). 391--400.

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

J. Pach and R. Pinchasi, A Long Non-Intersecting Path Among Disjoint Segments in the Plane, Combinatorial and computational geometry , 495--500, Math. Sci. Res. Inst. Publ., {\bf 52}, Cambridge Univ. Press, Cambridge, 2005.

H. Last and R. Pinchasi> At Least $n-1$ Intersection Points Among $n$ Unit Circles Disc. and Comp. Geom. .

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

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), 399--441.

R. Pinchasi and G. Rote, On the maximum size of an anti-chain of $k$-sets and convex pseudo-discs .

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

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

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

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

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

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

R. Pinchasi, Linear Algebra Approach to Geometric Graphs. JCT-A.

I. Ben-Dan, R. Pinchasi, and R. Ziv, Points with large $\alpha$-depth. .

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

S. Buzaglo, R. Pinchasi, and G. Rote, Topological Hyper-graphs. .

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

I. Ben-Dan, R. Pinchasi, R. Ziv On a problem of Felsner about quadrant depth.. .

R. Apfelbaum, I. Ben-Dan, S. Felsner, T. Miltzow, R. Pinchasi, T. Ueckerdt, R. Ziv, Points with large quadrant depth. .

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

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.

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

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. .

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

R. Pinchasi and A. Pinkus, Dominating Subsets under Projections. SIAM J. Discrete Math. 24 (2010), no. 3, 910--920.

E. Ackerman, T. Gelander, R. Pinchasi, Ice-Creams and Wedge Graphs. .

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

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

R. Pinchasi, The Zone Theorem Revisited. .

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

R. Pinchasi, A finite family of pseudo-discs must include a ``small'' pseudo-disc. .

R. Pinchasi, G. Wolansky, A generalization of Thue's theorem to packings of non-equal discs, and an application to a discrete approximation of entropy. .

R. Pinchasi, A Note on Smaller Fractional Helly Numbers. .

A. Oren, I. Pak, R. Pinchasi, On the Odd Area of Planar Sets. .

S. Moran, R. Pinchasi, Matchings vs hitting sets among half-spaces in low dimensional euclidean spaces. .

R. Pinchasi, Y. Rabinovich, {polygons: odd compression ratio and odd plane coverings} polygons: odd compression ratio and odd plane coverings .

R. Pinchasi, A theorem on unit segments on the real line. .

R. Pinchasi and A. Polyanskii, A one-page solution of a problem of Erd\H os and Purdy. .

R. Pinchasi, An algebraic solution of a problem of Erd\H os and Purdy. .

Ch. Keller and R. Pinchasi, On sets $n$ of points in general position that determine lines that can be pierced by $n$ points. .

M. Makhul, R. Pinchasi, On sets of points in general position that lie on a cubic curve in the plane and determine lines that can be pierced by few points .

R. Pinchasi, On the Odd Area of the Unit Disc.

R. Pinchasi and Amir Carmel, Some Notes about the Odd Area of Unit Discs Centered at Points on a Circle.

R. Pinchasi and Oren Yerushakmi, Covering the edges of a complete geometric graph with convex polygons.

R. Pinchasi, A note on lenses in arrangements of pairwise intersecting circles in the plane.

### 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.)

D. J. Kleitman, R. Pinchasi, A Note on the Number of Bichromatic Lines, unpublished preprint.

A link to the website of Avital Frumkin

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