On Cartesian skeletons of graphs

@article{Hammack2009OnCS,
  title={On Cartesian skeletons of graphs},
  author={Richard H. Hammack and Wilfried Imrich},
  journal={Ars Math. Contemp.},
  year={2009},
  volume={2},
  pages={191-205}
}
Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a notion of a Cartesian skeleton which transfers their multiplication properties to the Cartesian product… CONTINUE READING

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