[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
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 > Data Structures and Algorithms

arXiv:2003.04254 (cs)
[Submitted on 9 Mar 2020 (v1), last revised 19 Jul 2022 (this version, v2)]

Title:b-Coloring Parameterized by Clique-Width

Authors:Lars Jaffke, Paloma T. Lima, Daniel Lokshtanov
View PDF
Abstract:We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva [Algorithmica, 2018] and Bonomo et al. [Graphs Combin., 2009]. This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound. The running times of the clique-width based algorithms for b-Coloring and Fall Coloring are tight under the Exponential Time Hypothesis.
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM)
MSC classes: 05C85, 05C15
ACM classes: F.2.2; G.2.2
Cite as: arXiv:2003.04254 [cs.DS]
  (or arXiv:2003.04254v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2003.04254

Submission history

From: Lars Jaffke [view email]
[v1] Mon, 9 Mar 2020 16:58:43 UTC (83 KB)
[v2] Tue, 19 Jul 2022 09:09:00 UTC (189 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cs.DS
< prev   |   next >
new | recent | 2020-03
Change to browse by:
cs
cs.DM

References & Citations

DBLP - CS Bibliography

listing | bibtex
Lars Jaffke
Paloma T. Lima
Daniel Lokshtanov
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?)