### Vertex partition of hypergraphs and maximum degenerate subhypergraphs

#### Abstract

In 2007 Matamala proved that if *G* is a simple graph with maximum degree Δ ≥ 3 not containing *K*_{Δ+1} as a subgraph and *s*, *t* are positive integers such that *s*+*t* ≥ Δ, then the vertex set of *G* admits a partition (*S*,*T*) such that *G*[*S*] is a maximum order (*s*-1)-degenerate subgraph of *G* and *G*[*T*] is a (*t*-1)-degenerate subgraph of G. This result extended earlier results obtained by Borodin, by Bollobas and Manvel, by Catlin, by Gerencser and by Catlin and Lai. In this paper we prove a hypergraph version of this result and extend it to variable degeneracy and to partitions into more than two parts, thereby extending a result by Borodin, Kostochka, and Toft.

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PDFDOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.1

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