Talk:Kernelization

Latest comment: 7 years ago by InternetArchiveBot in topic External links modified

vertex cover - step 3

edit

Sorry for my probably incorrect edit, but I still don't understand why the following is needed in step 3: "In this case, the graph may be replaced by the complete graph  , which also has no  -vertex cover".

  • First, I am not sure I understand why this is correct. For example, if   then we have  , which is a triangle and has a 2-vertex cover.
  • Second, this step seems much more complicated than necessary. Why not just replace the graph with any non-empty graph and decrease $k$ to 0, for example?

--Erel Segal (talk) 06:34, 19 October 2014 (UTC)Reply

First, perhaps it should be  , and second, that would be ok too, as long as it can be described more simply. What I objected to in the earlier edit was replacing step 3 by aborting the algorithm. Of course one would do that in practice, and we should probably say so, but it doesn't fit the actual definition of a kernelization. —David Eppstein (talk) 06:36, 19 October 2014 (UTC)Reply

If you use   then at step #1 you remove all vertices one by one (since all of them have degree more than k) until you have 2 vertices with k=0, but then the promise of having less than   edges is not satisfied! Do you have an idea how to correct this? --Erel Segal (talk) 11:36, 19 October 2014 (UTC)Reply

vertex cover - step 1

edit

"If v is a vertex of degree greater than k, remove v from the graph and decrease k by one" - this seems problematic since k might be 0. --Erel Segal (talk) 11:32, 19 October 2014 (UTC)Reply

edit

Hello fellow Wikipedians,

I have just modified one external link on Kernelization. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 18:31, 4 May 2017 (UTC)Reply