## Abstract

Let H and G be graph classes. We say that H has the Erd?os-Pósa property for G if for any graph G ∈ G, the minimum vertex covering of all H-subgraphs of G is bounded by a function f of the maximum packing of H-subgraphs in G (by H-subgraph of G we mean any subgraph of G that belongs to H). In his monograph "Graph Theory", R. Diestel proves that if H is the class of all graphs that can be contracted to a fixed planar graph H, then H has the Erdös-Pósa property for the class of all graphs (with an exponential bounding function). In this note, we give an alternative proof of this result with a better (still exponential) bounding function. Our proof, for the case when G is some non-trivial minor-closed graph class, yields a low degree polynomial bounding function f. In particular f(k) = O(k^{1.5}).

Original language | English (US) |
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Pages | 2-6 |

Number of pages | 5 |

State | Published - 2008 |

Event | 7th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2008 - Gargnano, Italy Duration: May 13 2008 → May 15 2008 |

### Conference

Conference | 7th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2008 |
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Country/Territory | Italy |

City | Gargnano |

Period | 5/13/08 → 5/15/08 |

## Keywords

- Erdos-Pósa property
- Graph covering
- Graph packing
- Treewidth

## ASJC Scopus subject areas

- Control and Optimization
- Discrete Mathematics and Combinatorics