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, 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 , accepted.
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. 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), 399--441.
R. Pinchasi and G. Rote, On the maximum size of an anti-chain of $k$-sets and convex pseudo-discs 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. JCT-A.
I. Ben-Dan, 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 Hyper-graphs. submitted.
S. Buzaglo, R. Holzman, and R. Pinchasi, On $k$-intersecting curves and related problems. submitted.
I. Ben-Dan, R. Pinchasi, R. Ziv On a problem of Felsner about quadrant depth.. submitted.
R. Apfelbaum, I. Ben-Dan, 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, 910--920.
E. Ackerman, T. Gelander, R. Pinchasi, Ice-Creams 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, Hitting-Set 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 pseudo-discs must include a ``small'' pseudo-disc. submitted.
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. 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.)

D. J. Kleitman, R. Pinchasi, A Note on the Number of Bichromatic Lines, unpublished preprint.

A link to the website of Avital Frumkin