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Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture: In this paper, we show that every (2^{n-1}+1)-vertex

2019-07-28 00:56:37

Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture: In this paper, we show that every (2^{n-1}+1)-vertex induced subgraph of the n-dimensional cube graph has maximum degree at least sqrt{n}. This result is best possible, and improves a logarithmic lower bound shown by Chung, Füredi, Graham and Seymour in 1988. As a direct consequence, we prove that the sensitivity and degree of a boolean function are polynomially related, solving an outstanding foundational problem in theoretical computer science, the Sensitivity Conjecture of Nisan and Szegedy. Huang, Hao.

Source: arxiv.org

sensitivity conjecture induced degree hypercubes füredi boolean vertex