Multiplicative graphs and semi-lattice endomorphisms in the category of graphs

  title={Multiplicative graphs and semi-lattice endomorphisms in the category of graphs},
  author={Claude Tardif},
  journal={J. Comb. Theory, Ser. B},
A graph K is called multiplicative if whenever a categorical product of two graphs admits a homomorphism to K, then one of the factors also admits a homomorphism to K. We prove that all circular graphs Kk/d such that k/d < 4 are multiplicative. This is done using semi-lattice endomorphism in (the skeleton of) the category of graphs to prove the multiplicativity of some graphs using the known multiplicativity of the odd cycles. 
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