YYYelena Yuditsky
Yelena Yuditsky
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Yelena Yuditsky has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Marcin Witkowski
Adam Mickiewicz University
1 shared publication - Martin Merker
Technical University of Denmark
1 shared publication - Shakhar Smorodinsky
Ben-Gurion University of the Negev, Be’er-Sheva, Israel
1 shared publication - Tereza Klimošová
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
1 shared publication - Thomas Bellitto
Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark
1 shared publication
Latest Publications
- 24 July 2021
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 37 (6) , 2595-2599
Counterexamples to Thomassen’s Conjecture on Decomposition of Cubic Graphs
- 24 July 2021
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 37 (6) , 2595-2599
Counterexamples to Thomassen’s Conjecture on Decomposition of Cubic Graphs
- Open Access
Polychromatic Coloring for Half-Planes
We prove that for every integer $k$, every finite set of points in the plane can be $k$-colored so that every half-plane that contains at least $2k-1$ points, also contains at least one point from every color class. We also show that the bound $2k-1$ is best possible. This improves the best previously known lower and upper bounds of $\frac{4}{3}k$ and $4k-1$ respectively. We also show that every finite set of half-planes can be $k$ colored so that if a point $p$ belongs to a subset $H_p$ of at least $3k-2$ of the half-planes then $H_p$ contains a half-plane from every color class. This improves the best previously known upper bound of $8k-3$. Another corollary of our first result is a new proof of the existence of small size $\eps$-nets for points in the plane with respect to half-planes.Open AccessPolychromatic Coloring for Half-Planes
We prove that for every integer $k$, every finite set of points in the plane can be $k$-colored so that every half-plane that contains at least $2k-1$ points, also contains at least one point from every color class. We also show that the bound $2k-1$ is best possible. This improves the best previously known lower and upper bounds of $\frac{4}{3}k$ and $4k-1$ respectively. We also show that every finite set of half-planes can be $k$ colored so that if a point $p$ belongs to a subset $H_p$ of at least $3k-2$ of the half-planes then $H_p$ contains a half-plane from every color class. This improves the best previously known upper bound of $8k-3$. Another corollary of our first result is a new proof of the existence of small size $\eps$-nets for points in the plane with respect to half-planes.