Coloring Simple Hypergraphs
| dc.creator | Frieze, Alan | |
| dc.creator | Mubayi, Dhruv | |
| dc.date | 2008-09-17 | |
| dc.date | 2008-09-21 | |
| dc.date.accessioned | 2026-07-07T10:03:53Z | |
| dc.date.available | 2026-07-07T10:03:53Z | |
| dc.description | Fix an integer $k \ge 3$. A $k$-uniform hypergraph is simple if every two edges share at most one vertex. We prove that there is a constant $c$ depending only on $k$ such that every simple $k$-uniform hypergraph $H$ with maximum degree $\D$ has chromatic number satisfying $$χ(H) <c (\frac{\D}{\log \D})^{\frac{1}{k-1}}.$$ This implies a classical result of Ajtai-Komlós-Pintz-Spencer-Szemerédi and its strengthening due to Duke-Lefmann-Rödl. The result is sharp apart from the constant $c$. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0809.2979 | |
| dc.identifier | http://arxiv.org/abs/0809.2979 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169459 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D40 | |
| dc.title | Coloring Simple Hypergraphs | |
| dc.type | text |