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Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Dec 19, 2012 at 9:40 comment added Roland Bacher @domotorp: I got effectively a little bit confused about complexity-issues for perfect matchings: part of the confusion arose out of the similar notions of maximal matching (a matching which cannot be extended to a larger matching) and maximum matching (involving the largest possible number of edges). I first believed that only finding a maximal matching is in P (which is of course easy).
Dec 18, 2012 at 19:01 comment added Tony Huynh @domotorp: I think it was an honest mistake by Roland, since he must have assumed that you meant that finding a perfect matching is only in P for graphs of maximum degree 4. Indeed, the main point of my answer was just to clear up this confusion.
Dec 18, 2012 at 18:49 comment added domotorp Why would you write that after my comment it seems that finding a matching is NP-complete when I wrote that it is in P? Whatever...
Dec 18, 2012 at 17:20 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 17:16 vote accept Roland Bacher
Dec 18, 2012 at 16:59 answer added Tony Huynh timeline score: 2
Dec 18, 2012 at 16:52 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 16:37 history edited Emil Jeřábek CC BY-SA 3.0
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Dec 18, 2012 at 15:44 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 15:36 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 15:29 comment added Roland Bacher @domotorp: Your first comment refers to a bugged version containing the wrong definition, I have corrected it since. I do not know if this answers your second question. But if finding a matching in an arbitrary graph is in P the answer to my question is YES (you cannot suppose that the degree is $4$ however).
Dec 18, 2012 at 15:24 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 15:22 comment added domotorp I also don't see why this question is similar to the grid-matching problem, but if you remove the intersection condition there, then it is just about finding a matching in a graph (with max degree 4), so it is in P.
Dec 18, 2012 at 15:17 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 15:16 comment added domotorp I don't get it - if A has a row or column with an odd number of 1's, it cannot have an even sign configuration, while if this is not the case, you can pick M=A.
Dec 18, 2012 at 15:09 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 15:04 history edited Roland Bacher CC BY-SA 3.0
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Dec 18, 2012 at 14:30 history asked Roland Bacher CC BY-SA 3.0