TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Schweser, Thomas
A1  - Stiebitz, Michael
T1  - Partitions of hypergraphs under variable degeneracy constraints
JF  - Journal of Graph Theory
N2  - 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.
AB  - 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.
Y1  - 2025
SN  - 0364-9024
SS  - 0364-9024
U6  - https://doi.org/https://doi.org/10.1002/jgt.22575
DO  - https://doi.org/https://doi.org/10.1002/jgt.22575
VL  - 96
IS  - 1
SP  - 7
EP  - 33
S1  - 27
PB  - Wiley
ER  -