Timeline for graphs with independence number = Shannon capacity
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2022 at 11:01 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed
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| Feb 14, 2014 at 17:31 | vote | accept | Tobias Fritz | ||
| Feb 14, 2014 at 17:31 | answer | added | Tobias Fritz | timeline score: 5 | |
| Jan 11, 2014 at 21:03 | comment | added | Tobias Fritz | @Graphth and everybody else: we have finally disproved all these conjectures and are currently in the process of revising our manuscript accordingly. The proof is somewhat indirect and actually does make use of the relationship to quantum information theory that we develop. I will compose a more detailed answer as soon as the updated manuscript is on the arXiv. | |
| Dec 18, 2012 at 8:31 | history | edited | Tobias Fritz | CC BY-SA 3.0 |
added 64 characters in body
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| Dec 12, 2012 at 18:22 | comment | added | Tobias Fritz | @Graphth: thanks a bunch, that's very helpful! We didn't know about that paper of Haemers. It will take us some time now to revise our paper now that we have this new information. Leave me a PM if we can use your real name in the acknowledgments. | |
| Dec 10, 2012 at 18:47 | comment | added | GeoffDS | By the way, did you know that if you do @Graphth before your response, then it will notify me of a response? I think since you wrote the question that it will notify you when I respond, even if I don't do @tobias | |
| Dec 10, 2012 at 18:46 | comment | added | GeoffDS | $\alpha(G) = \Theta(G)$ does not imply $\alpha(G) = \vartheta(G)$. Haemers gives a counterexample in "An Upper Bound for the Shannon Capacity of a Graph". | |
| Dec 8, 2012 at 17:32 | comment | added | Tobias Fritz | One can also ask whether $\alpha(G)=\Theta(G)$ implies $\alpha(G)=\vartheta(G)$; if this is true, then the other conjectures immediately follow from the basic properties of the Lovász number $\vartheta$. Alas, we haven't been able to answer any of these four questions yet; but since our work lies mainly in relating these questions to problems in the mathematical foundations of quantum mechanics, we also haven't tried really hard. Our paper should be on the arXiv within a few days; I will announce it here. | |
| Dec 8, 2012 at 16:32 | comment | added | GeoffDS | So, have you ever answered any of your above questions? I am interested in all 3 separately. | |
| Oct 7, 2012 at 21:43 | history | edited | Tobias Fritz | CC BY-SA 3.0 |
updated
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| Oct 5, 2012 at 16:47 | history | edited | Tobias Fritz | CC BY-SA 3.0 |
deleted 75 characters in body
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| Oct 5, 2012 at 2:15 | answer | added | Will Traves | timeline score: 3 | |
| Oct 4, 2012 at 20:25 | answer | added | Will Traves | timeline score: 1 | |
| Oct 4, 2012 at 19:31 | history | asked | Tobias Fritz | CC BY-SA 3.0 |