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 KΔ+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 Bollobás and Manvel, by Catlin, by Gerencsér 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.