 License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2012.206
URN: urn:nbn:de:0030-drops-34173
URL: https://drops.dagstuhl.de/opus/volltexte/2012/3417/
 Go to the corresponding LIPIcs Volume Portal

### Edge-disjoint Odd Cycles in 4-edge-connected Graphs

 pdf-format:

### Abstract

Finding edge-disjoint odd cycles is one of the most important problems in graph theory, graph algorithm and combinatorial optimization. In fact, it is closely related to the well-known max-cut problem. One of the difficulties of this problem is that the Erdös-Pósa property does not hold for odd cycles in general. Motivated by this fact, we prove that for any positive integer k, there exists an integer f(k) satisfying the following: For any 4-edge-connected graph G=(V,E), either G has edge-disjoint k odd cycles or there exists an edge set F subseteq E with |F| <= f(k) such that G-F is bipartite. We note that the 4-edge-connectivity is best possible in this statement. Similar approach can be applied to an algorithmic question. Suppose that the input graph G is a 4-edge-connected graph with n vertices. We show that, for any epsilon > 0, if k = O ((log log log n)^{1/2-epsilon}), then the edge-disjoint k odd cycle packing in G can be solved in polynomial time of n.

### BibTeX - Entry

```@InProceedings{kawarabayashi_et_al:LIPIcs:2012:3417,
author =	{Ken-ichi Kawarabayashi and Yusuke Kobayashi},
title =	{{Edge-disjoint Odd Cycles in 4-edge-connected Graphs}},
booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
pages =	{206--217},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-35-4},
ISSN =	{1868-8969},
year =	{2012},
volume =	{14},
editor =	{Christoph D{\"u}rr and Thomas Wilke},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
DROPS-Home | Fulltext Search | Imprint | Privacy 