Existence of spanning $\mathcal{F}$-free subgraphs with large minimum degree

Guillem Perarnau; Bruce Reed

Existence of spanning $\mathcal{F}$-free subgraphs with large minimum degree

Combinatorics 2016-12-12 v2

Authors: Guillem Perarnau , Bruce Reed

Abstract

Let $\mathcal{F}$ be a family of fixed graphs and let $d$ be large enough. For every $d$ -regular graph $G$ , we study the existence of a spanning $\mathcal{F}$ -free subgraph of $G$ with large minimum degree. This problem is well-understood if $\mathcal{F}$ does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs.

Keywords

spanning subgraphs f-free graphs minimum degree regular graphs bipartite graphs extremal graph theory asymptotic results

Cite

@article{arxiv.1404.7764,
  title  = {Existence of spanning $\mathcal{F}$-free subgraphs with large minimum degree},
  author = {Guillem Perarnau and Bruce Reed},
  journal= {arXiv preprint arXiv:1404.7764},
  year   = {2016}
}

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22 pages

Existence of spanning $\mathcal{F}$-free subgraphs with large minimum degree

Abstract

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