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The Implicit Graph Conjecture is False
[article]
2021
arXiv
pre-print
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^O(nlog(n)) graphs on n vertices, and thus has at most factorial speed of growth. The Implicit Graph
arXiv:2111.13198v2
fatcat:3l2gfon2frgwfg76opn3cke7vm