DROPS

Document

DOI: 10.4230/LIPIcs.STACS.2017.28

Independent Sets near the Lower Bound in Bounded Degree Graphs

Authors: Zdenek Dvorák and Bernard Lidický

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract

By Brook's Theorem, every n-vertex graph of maximum degree at most Delta >= 3 and clique number at most Delta is Delta-colorable, and thus it has an independent set of size at least n/Delta. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an independent set of size at least n/Delta+k has a kernel of size O(k).

Cite as

Zdenek Dvorák and Bernard Lidický. Independent Sets near the Lower Bound in Bounded Degree Graphs. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{dvorak_et_al:LIPIcs.STACS.2017.28,
  author =	{Dvor\'{a}k, Zdenek and Lidick\'{y}, Bernard},
  title =	{{Independent Sets near the Lower Bound in Bounded Degree Graphs}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.28},
  URN =		{urn:nbn:de:0030-drops-70042},
  doi =		{10.4230/LIPIcs.STACS.2017.28},
  annote =	{Keywords: independent set, bounded degree, Delta-colorable, fixed parameter tractability}
}

Document

DOI: 10.4230/LIPIcs.STACS.2010.2469

The k-in-a-path Problem for Claw-free Graphs

Authors: Jiri Fiala, Marcin Kaminski, Bernard Lidický, and Daniël Paulusma

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract

Testing whether there is an induced path in a graph spanning $k$ given vertices is already \NP-complete in general graphs when $k=3$. We show how to solve this problem in polynomial time on claw-free graphs, when $k$ is not part of the input but an arbitrarily fixed integer.

Cite as

Jiri Fiala, Marcin Kaminski, Bernard Lidický, and Daniël Paulusma. The k-in-a-path Problem for Claw-free Graphs. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 371-382, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

Copy BibTex To Clipboard

@InProceedings{fiala_et_al:LIPIcs.STACS.2010.2469,
  author =	{Fiala, Jiri and Kaminski, Marcin and Lidick\'{y}, Bernard and Paulusma, Dani\"{e}l},
  title =	{{The k-in-a-path Problem for Claw-free Graphs}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{371--382},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2469},
  URN =		{urn:nbn:de:0030-drops-24692},
  doi =		{10.4230/LIPIcs.STACS.2010.2469},
  annote =	{Keywords: Induced path, claw-free graph, polynomial-time algorithm}
}

Search Results

Documents authored by Lidický, Bernard

Independent Sets near the Lower Bound in Bounded Degree Graphs

Abstract

Cite as

The k-in-a-path Problem for Claw-free Graphs

Abstract

Cite as

Thanks for your feedback!

Could not send message