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- Determining $\Theta({\mathcal C}_{2k+1})$ for odd cycles is a central open problem in information theory and extremal combinatorics.
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- For ${\mathcal C}\_{5}$, Lovász famously proved $\Theta({\mathcal C}\_{5})=\sqrt{5}$, but no exact value is
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known for $\Theta({\mathcal C}_{7})$.
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known for $\Theta({\mathcal C}\_{7})$.
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- It is possible that $\Theta({\mathcal C}\_{2k+1})=\vartheta({\mathcal C}\_{2k+1})$ for all $k$,
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but this is currently open beyond $k=2$.
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@@ -57,10 +57,10 @@ channel whose confusability graph is $G$.
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problem. Computers in Algebra and Number Theory, American Mathematical Society, Providence,
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RI (1971), 97–108.
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-[L1979] Lovász, L. On the Shannon capacity of a graph. IEEE Transactions on Information Theory **25** (1979), 1–7.
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-[PS2018] Sven Polak, Alexander Schrijver. New lower bound on the Shannon capacity of $C_7$ from circular graphs. Information Processing Letters, 143 (2019), 37-40. arXiv:1808.07438.
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-[PS2018] Sven Polak, Alexander Schrijver. New lower bound on the Shannon capacity of $C\_7$ from circular graphs. Information Processing Letters, 143 (2019), 37-40. arXiv:1808.07438.
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-[MO2017] K.A. Mathew, P.R.J. Östergård. New lower bounds for the Shannon capacity of odd cycles. Designs,
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Codes and Cryptography, 84 (2017), 13–22.
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-[VZ2002] A. Vesel, J. Zerovnik. Improved lower bound on the Shannon capacity of $C_7$. Information Processing
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-[VZ2002] A. Vesel, J. Zerovnik. Improved lower bound on the Shannon capacity of $C\_7$. Information Processing
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