DIMACS
DIMACS REU 2014

General Information

me
Student: Peter Korcsok
Office: 444
School: Charles University in Prague
E-mail: peter.korcsok guess_what_is_here rutgers.edu
Projects: Binary Kakeya Sets
  $L(p,q)$-labeling of Interval Graphs

Binary Kakeya Sets

Project Description

For $x,y \in \{0,1\}^n$ we define the line $L_{x,y} = \{x^i \oplus y \mid i = 0, ..., n-1\}$ of direction $x$ where $x^i$ denotes the $i$-th rotation of $x$. We say that a set $S \subseteq \{0,1\}^n$ is a Kakeya set if for every $x \in \{0,1\}^n$ there exists $y \in \{0,1\}^n$ such that $L_{x,y} \subseteq S$. Michal Koucký asks for the smallest Kakeya set for a given $n$.

Previous work

Current activities

First week (June 2nd - June 6th)

Second week (June 9th - June 13th)

Third week (June 16th - June 20th)

Fourth week (June 23th - June 27th)

Fifth week (June 30th - July 4th)

Sixth week (July 7th - July 11th)

Week has not finished yet.

Seventh week (July 14th - July 18th)

Week has not started yet.

Coworkers

Back to top

$L(p,q)$-labeling of Interval Graphs

Project Description

Interval graphs are intersection graphs of a family of intervals of real numbers. $L(p,q)$-labeling of a graph $G$ is a mapping $l \colon V_G \to X$ where $X \subset \mathbb{Z}$ such that Finally, span of graph $G$ is the smallest number $k$ such that there exists $L(p,q)$-labeling of $G$ using $X = \{ 0, \dots, k \}$. In this project, we look for a formula for the span of $L(2,1)$ for the class of interval graphs and its connection to the chromatic number of the graph and the maximum degree of the graph.

Previous work

Current activities

See progress on Veronica's webpage.

Coworkers

Back to top

Presentations


Additional Information

My Mentor
  • Professor James Abello
        http://www.mgvis.com/
        http://www.mgvis.com/AbelloVitaResearchOct08.html