English

Vertex partition of hypergraphs and maximum degenerate subhypergraphs

Combinatorics 2018-07-09 v1

Abstract

In 2007 Matamala proved that if GG is a simple graph with maximum degree Δ3\Delta\geq 3 not containing KΔ+1K_{\Delta +1} as a subgraph and s,ts, t are positive integers such that s+tΔs+t \geq \Delta, then the vertex set of GG admits a partition (S,T)(S,T) such that G[S]G[S] is a maximum order (s1)(s-1)-degenerate subgraph of GG and G[T]G[T] is a (t1)(t-1)-degenerate subgraph of GG. This result extended earlier results obtained by Borodin, by Bollob\'as and Manvel, by Catlin, by Gerencs\'{e}r 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.

Keywords

Cite

@article{arxiv.1807.02308,
  title  = {Vertex partition of hypergraphs and maximum degenerate subhypergraphs},
  author = {Thomas Schweser and Michael Stiebitz},
  journal= {arXiv preprint arXiv:1807.02308},
  year   = {2018}
}

Comments

12 pages

R2 v1 2026-06-23T02:52:41.655Z