A counter-example to the probabilistic universal graph conjecture via randomized communication complexity

Lianna Hambardzumyan; Hamed Hatami; Pooya Hatami

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arXiv · 2111.10436

A counter-example to the probabilistic universal graph conjecture via randomized communication complexity

Lianna Hambardzumyan·Hamed Hatami·Pooya Hatami

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Abstract

We refute the Probabilistic Universal Graph Conjecture of Harms, Wild, and Zamaraev, which states that a hereditary graph property admits a constant-size probabilistic universal graph if and only if it is stable and has at most factorial speed. Our counter-example follows from the existence of a sequence of $n \times n$ Boolean matrices $M_n$, such that their public-coin randomized communication complexity tends to infinity, while the randomized communication complexity of every $\sqrt{n}\times \sqrt{n}$ submatrix of $M_n$ is bounded by a universal constant.

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BibTeX RIS

Lianna Hambardzumyan, Hamed Hatami, Pooya Hatami. 2021-11-19. A counter-example to the probabilistic universal graph conjecture via randomized communication complexity. https://arxiv.org/abs/2111.10436

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