Abstract
We consider the problem of estimating the Shannon capacity of a circulant graph C n,J of degree four with n vertices and chord length J, 2 ≤ J ≤ n, by computing its Lovász theta function θ(C n,J ). We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation.
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Brimkov, V.E., Barneva, R.P., Klette, R., Straight, J. (2004). Efficient Computation of the Lovász Theta Function for a Class of Circulant Graphs. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_24
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DOI: https://doi.org/10.1007/978-3-540-30559-0_24
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