• Corpus ID: 244708976

The Implicit Graph Conjecture is False

@article{Hatami2021TheIG,
  title={The Implicit Graph Conjecture is False},
  author={Hamed Hatami and Pooya Hatami},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.13198}
}
An efficient implicit representation of an n-vertex graph G in a family F of graphs assigns to each vertex of G a binary code of length O(log n) so that the adjacency between every pair of vertices can be determined only as a function of their codes. This function can depend on the family but not on the individual graph. Every family of graphs admitting such a representation contains at most 2 log(n)) graphs on n vertices, and thus has at most factorial speed of growth. The Implicit Graph… 
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