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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2012.432
URN: urn:nbn:de:0030-drops-33986
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3398/
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Fomin, Fedor V. ; Golovach, Petr A.

Parameterized Complexity of Connected Even/Odd Subgraph Problems

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Abstract

Cai and Yang initiated the systematic parameterized complexity study of the following set of problems around Eulerian graphs. For a given graph G and integer k, the task is to decide if G contains a (connected) subgraph with k vertices (edges) with all vertices of even (odd) degrees. They succeed to establish the parameterized complexity of all cases except two, when we ask about

- a connected k-edge subgraph with all vertices of odd degrees, the problem known as k-Edge Connected Odd Subgraph; and

- a connected k- vertex induced subgraph with all vertices of even degrees, the problem known as k-Vertex Eulerian Subgraph.

We resolve both open problems and thus complete the characterization of even/odd subgraph problems from parameterized complexity perspective. We show that k-Edge Connected Odd Subgraph is FPT and that k-Vertex Eulerian Subgraph is W[1]-hard.

Our FPT algorithm is based on a novel combinatorial result on the treewidth of minimal connected odd graphs with even amount of edges.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2012:3398,
  author =	{Fedor V. Fomin and Petr A. Golovach},
  title =	{{Parameterized Complexity of Connected Even/Odd Subgraph Problems}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{432--440},
  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},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3398},
  URN =		{urn:nbn:de:0030-drops-33986},
  doi =		{10.4230/LIPIcs.STACS.2012.432},
  annote =	{Keywords: Parameterized complexity, Euler graph, even graph, odd graph, treewidth}
}

Keywords: Parameterized complexity, Euler graph, even graph, odd graph, treewidth
Collection: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date: 2012
Date of publication: 24.02.2012

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