Good k-colorings have been defined by C. Berge who showed their existence in balanced hypergraphs. There is a simple generalization to oriented balanced hypergraphs: using the bi-coloring characterization of 0, ± 1-matrices of M. Conforti and G. Cornuejols, we show that oriented balanced hypergraphs have good k-colorings for any k. A stronger type of coloring is also shown to exist for oriented balanced hypergraphs. © 2006 Elsevier B.V. All rights reserved.
de Werra, D. (2006). Good and nice colorings of balanced hypergraphs. Discrete Mathematics, 306(19–20), 2630–2636. https://doi.org/10.1016/j.disc.2005.12.044