Work

Frames, $A$-paths and the Erdős-Pósa property

Year: 2017

Type: preprint

Abstract: A key feature of Simonovits' proof of the classic Erdős-Pósa theorem is a simple subgraph of the host graph, a frame, that determines the outcome of the theorem. We transfer this frame technique to $A$-paths. With it we deduce a simple proof of Gallai's theorem, although with a worse bound, and we verify the Erdős-Pósa property for long and for even $A$-paths. We also show that even $A$-paths do not have the edge-Erdős-Pósa property.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1707.02918

Authors: Bruhn, Henning, Heinlein, Matthias, Joos, Felix

Institutions: Universität Ulm, University of Birmingham

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Engineering and Physical Sciences Research Council

Awards: G4503969510, G5342091163, Randomized approaches to combinatorial packing and covering problems