The Domatic Number Problem on Some Perfect Graph Families

@article{Kaplan1994TheDN,
  title={The Domatic Number Problem on Some Perfect Graph Families},
  author={Haim Kaplan and Ron Shamir},
  journal={Inf. Process. Lett.},
  year={1994},
  volume={49},
  pages={51-56}
}
An extremely simple, linear time algorithm is given for constructing a domatic partition in totally balanced hypergraphs. This simpli es and generalizes previous algorithms for interval and strongly chordal graphs. On the other hand, the domatic number problem is shown to be NP-complete for several families of perfect graphs, including chordal and bipartite graphs. 
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Totally balanced and greedy matrices

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