Speaker
Prof.
György Kiss
(Eötvös Loránd University, Hungary)
Description
There are sevaral variations of vertex and edge colorings of hypergraphs.
A {\em vertex coloring\/} of a hypergraph ${\cal H}=(X,{\cal C})$ is a mapping $\phi $ from $X$ to a set of colors $\{1,2,\ldots ,k\} .$ A {\em strict\/ rainbow-free $k$-coloring\/} is a mapping $\phi :X\to\{1,\dots,k\}$ that uses each of the $k$ colors on at least one vertex such that each edge of ${\cal H}$ has at least two vertices with the same color. If $X_i=\phi ^{-1}(i),$ then a different but equivalent view is a {\em color partition\/} $X_1\cup cdots\cup X_k=X$ with $k$ nonempty classes. A coloring is called {\em balanced,} if $-1\leq |X_i|-|X_j| \leq 1$ holds for all $i\neq j.$
An \emph{edge coloring} of ${\cal H}$ with $k$ colors is a surjective function that assigns to edges of ${\cal H}$ a color from a $k$-set of colors. An edge coloring with $k$ colors is \emph{proper}, if for all intersecting pairs of edges have different colors. The \emph{chromatic index} $\chi'({\cal H})$ is the smallest number $k$ for which there exists a proper coloring of ${\cal H}$ with $k$ colors. A coloring with $k$ colors is \emph{complete} if each pair of colors appears on at least one vertex of ${\cal H}$. The \emph{pseudoachromatic index} $\psi'({\cal H})$
is the largest number $k$ for which there exist a complete coloring with $k$ colors, while the \emph{achromatic index} $\alpha'({\cal H})$ is the largest number $k$ for which there exist a proper and complete coloring with $k$ colors.
Let $\Pi $ be an $n$-dimensional finite affine or projective space and $0< d
Primary author
Prof.
György Kiss
(Eötvös Loránd University, Hungary)
