Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Discrete Mathematics

arXiv:cs/0405059 (cs)
[Submitted on 17 May 2004 (v1), last revised 9 Jan 2006 (this version, v4)]

Title:Erratum : MCColor is not optimal on Meyniel graphs

Authors:Benjamin Lévêque (Leibniz - IMAG), Frédéric Maffray (Leibniz - IMAG)
View PDF
Abstract: A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. In the manuscript "Coloring Meyniel graphs in linear time" we claimed that our algorithm MCColor produces an optimal coloring for every Meyniel graph. But later we found a mistake in the proof and a couterexample to the optimality, which we present here. MCColor can still be used to find a stable set that intersects all maximal cliques of a Meyniel graph in linear time. Consequently it can be used to find an optimal coloring in time O(nm), and the same holds for Algorithm MCS+Color. This is explained in the manuscript "A linear algorithm to find a strong stable set in a Meyniel graph" but this is equivalent to Hertz's algorithm. The current best algorithm for coloring Meyniel graphs is the O(n^2) algorithm LexColor due to Roussel and Rusu. The question of finding a linear-time algorithm to color Meyniel graphs is still open.
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
ACM classes: G.2.2
Cite as: arXiv:cs/0405059 [cs.DM]
  (or arXiv:cs/0405059v4 [cs.DM] for this version)
  https://doi.org/10.48550/arXiv.cs/0405059

Submission history

From: M. Benjamin Leveque [view email] [via CCSD proxy]
[v1] Mon, 17 May 2004 14:04:47 UTC (9 KB)
[v2] Mon, 18 Apr 2005 05:40:46 UTC (11 KB)
[v3] Thu, 15 Dec 2005 09:33:50 UTC (8 KB)
[v4] Mon, 9 Jan 2006 20:03:23 UTC (19 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
cs.DM
< prev   |   next >
new | recent | 2004-05

References & Citations

DBLP - CS Bibliography

listing | bibtex
Benjamin Lévêque
Frédéric Maffray
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)