Frames, $A$-paths and the Erd\H{o}s-P\'osa property
Combinatorics
2018-01-24 v3
Abstract
A key feature of Simonovits' proof of the classic Erd\H{o}s-P\'osa theorem is a simple subgraph of the host graph, a frame, that determines the outcome of the theorem. We transfer this frame technique to -paths. With it we deduce a simple proof of Gallai's theorem, although with a worse bound, and we verify the Erd\H{o}s-P\'osa property for long and for even -paths. We also show that even -paths do not have the edge-Erd\H{o}s-P\'osa property.
Keywords
Cite
@article{arxiv.1707.02918,
title = {Frames, $A$-paths and the Erd\H{o}s-P\'osa property},
author = {Henning Bruhn and Matthias Heinlein and Felix Joos},
journal= {arXiv preprint arXiv:1707.02918},
year = {2018}
}
Comments
16 pages. A number of small issues fixed, a table with results on paths and cycles added