Abstract
In this paper we study the edge-clique cover number of the tensor product K n ×K n . We derive an easy lowerbound for the edge-clique number of graphs in general. We prove that, when n is prime θ e (K n ×K n ) matches the lowerbound. Moreover, we prove that θ e (K n ×K n ) matches the lowerbound if and only if a projective plane of order n exists. We also show an easy upperbound for θ e (K n ×K n ) in general, and give its limiting value when the Riemann hypothesis is true.
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Hon, WK., Kloks, T., Liu, HH., Wang, YL. (2014). Edge-Clique Covers of the Tensor Product. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_7
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DOI: https://doi.org/10.1007/978-3-319-07956-1_7
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