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arXiv · 1807.02308

Vertex partition of hypergraphs and maximum degenerate subhypergraphs

Thomas Schweser·Michael Stiebitz
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Abstract

In 2007 Matamala proved that if $G$ is a simple graph with maximum degree $\Delta\geq 3$ not containing $K_{\Delta +1}$ as a subgraph and $s, t$ are positive integers such that $s+t \geq \Delta$, 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 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.

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Thomas Schweser, Michael Stiebitz. 2018-07-06. Vertex partition of hypergraphs and maximum degenerate subhypergraphs. https://arxiv.org/abs/1807.02308

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