@article{SchweserStiebitz2025,
  author    = {Schweser, Thomas and Stiebitz, Michael},
  title     = {Partitions of hypergraphs under variable degeneracy constraints},
  journal   = {Journal of Graph Theory},
  volume    = {96},
  number    = {1},
  publisher = {Wiley},
  issn      = {0364-9024},
  doi       = {https://doi.org/10.1002/jgt.22575},
  pages     = {7 -- 33},
  year      = {2025},
  abstract  = {The paper deals with partitions of hypergraphs into induced subhypergraphs satisfying constraints on their degeneracy. Our hypergraphs may have multiple edges, but no loops. Given a hypergraph and a sequence of vertex functions such that for all , we want to find a sequence of vertex disjoint induced subhypergraphs containing all vertices of such that each hypergraph is strictly -degenerate, that is, for every nonempty subhypergraph there is a vertex such that . Our main result in this paper says that such a sequence of hypergraphs exists if and only if is not a so-called hard pair. Hard pairs form a recursively defined family of configurations, obtained from three basic types of configurations by the operation of merging a vertex. Our main result has several interesting applications related to generalized hypergraph coloring problems.},
  language  = {en}
}