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.