Edge-Clique Covers of the Tensor Product

  • Wing-Kai Hon
  • Ton Kloks
  • Hsiang-Hsuan Liu
  • Yue-Li Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)


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.


Tensor Product Projective Plane Intersection Graph Riemann Hypothesis Clique Number 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Wing-Kai Hon
    • 1
  • Ton Kloks
    • 1
  • Hsiang-Hsuan Liu
    • 1
    • 3
  • Yue-Li Wang
    • 2
  1. 1.National Tsing Hua UniversityTaiwan
  2. 2.National Taiwan University of Science and TechnologyTaiwan
  3. 3.University of LiverpoolUK

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