# Toward a Hajnal-Szemeredi theorem for hypergraphs - Mathematics > Combinatorics

Toward a Hajnal-Szemeredi theorem for hypergraphs - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let $H$ be a triple system with maximum degree $d>1$ and let$r>10^7\sqrt{d}\log^{2}d$. Then $H$ has a proper vertex coloring with $r$colors such that any two color classes differ in size by at most one. The boundon $r$ is sharp in order of magnitude apart from the logarithmic factors.Moreover, such an $r$-coloring can be found via a randomized algorithm whoseexpected running time is polynomial in the number of vertices of $\cH$.This is the first result in the direction of generalizing theHajnal-Szemer\-edi theorem to hypergraphs.

Author: ** Hal Kierstead, Dhruv Mubayi**

Source: https://arxiv.org/