On the well-coveredness of Cartesian products of graphs

@article{Fradkin2009OnTW,
  title={On the well-coveredness of Cartesian products of graphs},
  author={Alexandra Ovetsky Fradkin},
  journal={Discrete Mathematics},
  year={2009},
  volume={309},
  pages={238-246}
}
A graph G is well-covered if every maximal independent set has the same cardinality. This paper investigates when the Cartesian product of two graphs is well-covered. We prove that if G and H both belong to a large class of graphs that includes all non-wellcovered triangle-free graphs and most well-covered triangle-free graphs, then G × H is not well-covered. We also show that if G is not well-covered, then neither is G × G. Finally, we show that G × G is not well-covered for all graphs of… CONTINUE READING
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