Lower bounds on the independence numbers of distance graphs with vertices in $\{-1, 0, 1\}^n$

A. R. Akhiiarov; A. V. Bobu; A. M. Raigorodskii

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arXiv · 2412.17120

Lower bounds on the independence numbers of distance graphs with vertices in $\{-1, 0, 1\}^n$

A. R. Akhiiarov·A. V. Bobu·A. M. Raigorodskii

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Abstract

This work is devoted to lower bounds on independence numbers of distance graphs with vertices in $\{-1,0,1\}^n$. The asymptotic case is studied, yielding new results over a broad range of parameters. Numerical results are presented, highlighting nontrivial relationships between the obtained bounds. Known upper bounds and their potential suboptimality are discussed separately.

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A. R. Akhiiarov, A. V. Bobu, A. M. Raigorodskii. 2025-02-19. Lower bounds on the independence numbers of distance graphs with vertices in $\{-1, 0, 1\}^n$. https://arxiv.org/abs/2412.17120

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