Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs

@article{Maninska2020QuantumII,
  title={Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs},
  author={Laura Man{\vc}inska and David E. Roberson},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={661-672}
}
  • L. Mančinska, D. Roberson
  • Published 2020
  • Computer Science, Physics, Mathematics
  • 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
Over 50 years ago, Lovász proved that two graphs are isomorphic if and only if they admit the same number of homomorphisms from any graph. Other equivalence relations on graphs, such as cospectrality or fractional isomorphism, can be characterized by equality of homomorphism counts from an appropriately chosen class of graphs. Dvořák [J. Graph Theory 2010] showed that taking this class to be the graphs of treewidth at most $k$ yields a tractable relaxation of graph isomorphism known as $k… Expand
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