Equitable coloring of k-uniform hypergraphs
| dc.creator | Yuster, Raphael | |
| dc.date | 2002-02-22 | |
| dc.date.accessioned | 2026-07-07T04:46:37Z | |
| dc.date.available | 2026-07-07T04:46:37Z | |
| dc.description | Let $H$ be a $k$-uniform hypergraph with $n$ vertices. A {\em strong $r$-coloring} is a partition of the vertices into $r$ parts, such that each edge of $H$ intersects each part. A strong $r$-coloring is called {\em equitable} if the size of each part is $\lceil n/r \rceil$ or $\lfloor n/r \rfloor$. We prove that for all $a \geq 1$, if the maximum degree of $H$ satisfies $Δ(H) \leq k^a$ then $H$ has an equitable coloring with $\frac{k}{a \ln k}(1-o_k(1))$ parts. In particular, every $k$-uniform hypergraph with maximum degree $O(k)$ has an equitable coloring with $\frac{k}{\ln k}(1-o_k(1))$ parts. The result is asymptotically tight. The proof uses a double application of the non-symmetric version of the Lovász Local Lemma. | |
| dc.description | 10 Pages | |
| dc.identifier | https://arxiv.org/abs/math/0202230 | |
| dc.identifier | http://arxiv.org/abs/math/0202230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63407 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C15 | |
| dc.title | Equitable coloring of k-uniform hypergraphs | |
| dc.type | text |