# Rom

Pinchasi

PhD

Research interests:

Combinatorics, Discrete Geometry, Computational Geometry, Topological Graphs

www2.math.technion.ac.il/~room/

## Publications

### Selected Papers:

- Gallai-Sylvester Theorem for Pairwise Intersecting Unit Circles, Discrete and Computational Geometry, 28 (2002), 607--624.
- 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 Politècnica de Catalunya, Barcelona, Spain. 123--132.
- 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.
- On the Complexity of Arrangements of Circles in the Plane, Discrete and Computational Geometry, {\bf 26} (2001), 465-492.
- On the Number of Balanced Lines, Discrete and Computational Geometry, {\bf 25} (2001), 611--628.
- Bichromatic Lines With Few Points, J. Combinatorial Theory Ser. A, {\bf 90} (2000), 326--335.
- Unit Equilateral Triangles Induced by Point Sets in Convex Position, American Mathematical Monthly, {\bf 110} (2003), 400--406.
- 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.
- 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.).
- Lines With Many Points On Both Sides, Discrete and Computational Geometry, {\bf 30} (2003), 415--435.
- 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.
- 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.).
- On Graphs that Do not Contains the Cube and Related Problems, Combinatorica, {\bf 25} (2005), no. 5, 615--623.
- Topological Graphs with no Large Grids, Graphs and Combinatorics, {\bf 21} (2005), no. 3, 355--364.
- A Note on the Existence of a Directions Path, Disc. and Comp. Geom. , {\bf 33} (2005), no. 2, 223--229.
- The Minimum Number of Edge-Directions of a Convex Polytope, J. Combinatorial Theory, ser. A. {\bf 107}, (2004), no. 1, 147--151.
- Crossing Patterns of Semi-Algebraic Sets, J. Combinatorial Theory, ser. A. {\bf 111} (2005), no. 2, 310--326.
- On The Delaunay Graph of a Geometric Graph, proc. 20th ACM Symp. on Computational Geometry, (2004). 378--382.
- 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.
- Forbidden $k$-Sets in the Plane, SIDMA.
- 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.
- At Least $n-1$ Intersection Points Among $n$ Unit Circles, Disc. and Comp. Geom.
- 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.
- On Some Isoperimetric Inequality In The Universal Covering Space Of The Punctured Plane, Discrete Mathematics.
- There are not too many Magic Configurations, Discrete Comput. Geom.
- Geometric Graphs with no Two Parallel Edges, Combinatorica.
- How to cut out a convex polyhedron, submitted. And a shorter version just of the main Lemma:Collapsing walls theorem, American Mathematical Monthly.
- On inducing polygons and related problems, submitted. And a shorter paper with the shorter proof only:
- Regular Matchstick Graphs, American Mathematical Monthly.
- Dominating Subsets under Projections, SIAM J. Discrete Math. 24 (2010), no. 3, 910--920.

### Unpublished manuscripts:

- A Note on the Number of Bichromatic Lines, unpublished preprint.