For a given hypergraph $H$ with chromatic number $\chi(H)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) $\{E_1,E_2,\ldots,E_l\}$ for $E(H)$, such that the hypergraph induced by $E_i$ for each $1\leq i\leq l$ is $k$-colorable, is $\lceil \log_{k} \chi(H) \rceil$.
B. D. Acharya (1983). Even edge colorings of a graph. J. Combin.
Theory Ser. B. 35, 78-79 N. Alon and Y. Egawa (1985). Even edge colorings of a graph. J. Combin.
Theory Ser. B. 38, 93-94
Omidi, G., & Tajbakhsh, K. (2014). Decomposing hypergraphs into $k$-colorable hypergraphs. Transactions on Combinatorics, 3(2), 31-33. doi: 10.22108/toc.2014.5146
MLA
Gholamreza Omidi; Khosro Tajbakhsh. "Decomposing hypergraphs into $k$-colorable hypergraphs". Transactions on Combinatorics, 3, 2, 2014, 31-33. doi: 10.22108/toc.2014.5146
HARVARD
Omidi, G., Tajbakhsh, K. (2014). 'Decomposing hypergraphs into $k$-colorable hypergraphs', Transactions on Combinatorics, 3(2), pp. 31-33. doi: 10.22108/toc.2014.5146
VANCOUVER
Omidi, G., Tajbakhsh, K. Decomposing hypergraphs into $k$-colorable hypergraphs. Transactions on Combinatorics, 2014; 3(2): 31-33. doi: 10.22108/toc.2014.5146
)