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

@article{Tardif2005MultiplicativeGA, title={Multiplicative graphs and semi-lattice endomorphisms in the category of graphs}, author={Claude Tardif}, journal={J. Comb. Theory, Ser. B}, year={2005}, volume={95}, pages={338-345} }

- Published 2005 in J. Comb. Theory, Ser. B
DOI:10.1016/j.jctb.2005.06.002

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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