| author: | Gordana Manić and Yoshiko Wakabayashi |
|---|---|
| title: | Packing triangles in low degree graphs and indifference graphs |
| keywords: | triangle packing, approximation algorithm, polynomial algorithm, low degree graph, indifference graph |
| abstract: |
We consider the problems of finding the maximum number of
vertex-disjoint triangles (VTP) and edge-disjoint triangles
(ETP) in a simple graph. Both problems are NP-hard. The
algorithm with the best approximation guarantee known so
far for these problems has ratio
3/2 + ɛ
, a result that follows from a more general algorithm
for set packing obtained by Hurkens and Schrijver in 1989.
We present improvements on the approximation ratio for
restricted cases of
VTP
and
ETP
that are known to be APX-hard: we give an
approximation algorithm for
VTP
on graphs with maximum degree
4
with ratio slightly less than
1.2
, and for
ETP
on graphs with maximum degree
5
with ratio
4/3
. We also present an exact linear-time algorithm for
VTP
on the class of indifference graphs.
|
| If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |
| reference: | Gordana Manić and Yoshiko Wakabayashi (2005), Packing triangles in low degree graphs and indifference graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 251-256 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dmAE0150.ps.gz (87 K) |
| ps-source: | dmAE0150.ps (241 K) |
| pdf-source: | dmAE0150.pdf (184 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.