Talk:Vertex cover

Tree Minimal Vertex Cover

The reference to [1] contains an error in the algorithm as explained by mmiguel.martin. I added an alternative algroithm that suppose to do that but I didn't find any reference, I found the algorithm in a test solution of a course in the Open University of Israel. — Preceding unsigned comment added by 37.46.41.87 (talk) 11:42, 4 June 2016 (UTC)

Merge hitting set to set cover?

Should we merge everything from Vertex cover#Vertex cover in hypergraphs (and k-approximation of k-hitting set) to Set cover problem? The current situation is strange, as different aspects of the approximability of the set cover problem are discussed in different articles. — Miym (talk) 22:41, 9 November 2009 (UTC)

Hitting Set and Set Cover are two different views on the same problem. However, I think that the bounded edge size view on hitting set is more natural than the bounded frequency view on set cover. Therefore, I'd vote to merge k-approximation of k-hitting set into Vertex cover#Vertex cover in hypergraphs and tidy up the situation in Set cover problem a little. Agreed? ylloh (talk) 14:18, 11 November 2009 (UTC)

• To give some examples of how other sources handle this confusion, see [2] and [3]. Vazirani's textbook ("Approximation Algorithms", Springer 2003) seems to present everything (including k-approximation of k-hitting set) from the perspective of set covering. — Miym (talk) 14:55, 11 November 2009 (UTC)

In a textbook or a lecture, it's good to only have few example problems since they are to be read or taught from start to end. This does not hold for wikipedia. Also I wouldn't want to do it like wwwcompendium as this may not be a good example. ylloh (talk) 14:40, 13 November 2009 (UTC)

I don't know much about the subject matter, but k-approximation of k-hitting set should definitely be merged with something else. --Robin (talk) 20:06, 12 November 2009 (UTC)

Claim not supported by reference

The article claimed that vertex cover remains NP-complete

even in planar graphs of degree at most 3.

with a reference to Garey and Johnson (1977). I checked my copy and the claim is not supported there. According to page 190 it is the problem of connected vertex cover (where the set of vertices is required to be connected) that remains NP-complete for planar graphs. So I removed the claim. Gdr 10:42, 23 March 2012 (UTC)

Look again. On p.190 it says that vertex cover has the same complexity as independent set for any class of graphs and on p.195 it says that independent set is NP-complete for planar 3-regular graphs. —David Eppstein (talk) 17:46, 23 March 2012 (UTC)

Thanks, David. Sorry to have misunderstood. Gdr 13:44, 27 April 2012 (UTC)

Definition

In this section, the second of the two "vertex covers" seems to fail to meet the definition. Am I missing something? 73.32.71.188 (talk) 14:40, 7 April 2021 (UTC)

The top and the middle graph are considered to be counter examples ("none with fewer"); the bottom graph is an example. - Jochen Burghardt (talk) 14:58, 7 April 2021 (UTC)

It would be less confusing if only the bottom graph could be shown. Can sombody perform an appropriate crop? Commons doesn't support cropping svg images. - Jochen Burghardt (talk) 15:02, 7 April 2021 (UTC)

I think OP was talking about this image listed in the definition, where the rightmost graph clearly does not denote a vertex cover. 2603:8080:1301:D535:FC5D:E3C:17ED:4287 (talk) 01:31, 23 April 2021 (UTC)

Oops, yes you are right. A new image version was uploaded on 6 Apr 2021, which had an (uncovered) extra edge. I just reverted that upload. - Jochen Burghardt (talk) 06:57, 23 April 2021 (UTC)

Wikidata links

Apparently, there are two different wikidata links, viz d:Q11515519 = vertex cover and d:Q924362 = vertex cover problem. I guess they should be merged, however, I don't know how to merge wikidata entries.

Moreover, the wikipedia link sets attached to the wikidata entries are not disjoint, their intersection is { de, it, ja, pl, ru }. In each of these languages, there exists one article about vertex cover, and another one about the vertex cover problem; in de and ru, one is a redirect to the other. So merging would require discussion in it, ja, pl - no idea how to find editors that are capable of these languages. - Jochen Burghardt (talk) 20:57, 15 November 2023 (UTC)

It is easy to merge wikidata entries when they are truly duplicates but should not be done for somewhat distinct topics with overlapping content such as this case, because some other languages' Wikipedias separate the two items into two different articles. —David Eppstein (talk) 21:05, 15 November 2023 (UTC)