Partitions of hypergraphs under variable degeneracy constraints

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 H and a sequence f=(f1,f2, horizontal ellipsis ,fp) of p >= 1 vertex functions fi:V(H)-> N0 such that f1(v)+f2(v)+MIDLINE HORIZONTAL ELLIPSIS+fp(v)>= dH(v) for all v is an element of V(H), we want to find a sequence (H1,H2, horizontal ellipsis ,Hp) of vertex disjoint induced subhypergraphs containing all vertices of H such that each hypergraph Hi is strictly fi-degenerate, that is, for every nonempty subhypergraph H 'subset of Hi there is a vertex v is an element of V(H ') such that dH '(v)

Automated summary

The paper addresses the partitioning of hypergraphs into induced subhypergraphs with constraints on their degeneracy under vertex functions. The goal is to find a sequence of vertex-disjoint induced subhypergraphs containing all vertices of the hypergraph, each of which is strictly degenerate based on the respective vertex function.