Talk:Edge cover

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Computer science Mid‑importance

This article is within the scope of WikiProject Computer science, a collaborative effort to improve the coverage of Computer science related articles on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.Computer scienceWikipedia:WikiProject Computer scienceTemplate:WikiProject Computer scienceComputer science articles

Mid

This article has been rated as Mid-importance on the project's importance scale.

Things you can help WikiProject Computer science with:

Here are some tasks awaiting attention:

Article requests :
- Requested articles/Applied arts and sciences/Computer science, computing, and Internet
Cleanup :
- Computer science articles needing attention
- Computer science articles needing expert attention
Copyedit :
- Computing
Expand :
- Computer science
Infobox :
- Computer science articles without infoboxes
Maintain :
- Timeline of computing 2020–present
Photo :
- Find pictures for the biographies of computer scientists (see List of computer scientists)
- Computing articles needing images
Stubs :
- Computer science stubs
Unreferenced :
- WikiProject Computer science/Unreferenced BLPs
Project-related :
- Tag all relevant articles in Category:Computer science and sub-categories with {{WikiProject Computer science}}

Greedy Algorithm

Can I get a citation for the greedy algorithm? I think it's not correct. Suppose a graph with four nodes V = {a,b,c,d} that form a line, i.e. E = {(a,b),(b,c),(c,d)}. Choosing (b,c) forms a maximal matching, but there is no way to greedily extend it to a minimal edge cover (that is {(a,b),(c,d)} in this graph). I googled around a bit but found nothing relevant. --134.96.156.86 (talk)

Never mind. I always get maximAL and maximUM matchings confused. --134.96.156.86 (talk) —Preceding undated comment added 11:40, 21 December 2009 (UTC).[reply]

Right. Regarding citations, e.g. in [1] you can find the theorem "the size of the minimum edge cover plus the size of the maximum number of independent edges equals the number of vertices of a graph"; note that "independent edges" = "matching". An easy way to prove this theorem is to consider the simple algorithm that greedily extends a maximum matching; once you have established the correctness of the algorithm, this theorem follows as a simple corollary (and vice versa). I think we could discuss this connection in more detail on this page. — Miym (talk) 17:54, 21 December 2009 (UTC)[reply]