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In this short note we study two questions about the existence of subgraphs of the hypercube $Q_n$ with certain properties.
The theory of error-correcting codes
Florence Jessie MacWilliams and Neil James Alexander Sloane · 1977
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The concept of leverage in network vulnerability
KS Bagga, LW Beineke, MJ Lipman, and RE Pippert · 1991
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The integrity of the cube is small
Lowell W Beineke, Wayne Goddard, Peter Hamburger, Daniel J Kleitman, Marc J Lipman, and Raymond E Pippert · 1991
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A survey of integrity
Kunwarjit S Bagga, Lowell W Beineke, WD Goddard, Marc J Lipman, and Raymond E Pippert · 1992
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Hypercube subgraphs with minimal detours
Pál Erdős, Peter Hamburger, Raymond E Pippert, and William D Weakley · 1996
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Sparse distance preservers and additive spanners
Béla Bollobás, Don Coppersmith, and Michael Elkin · 2005
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David P Woodruff · 2006
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On k-detour subgraphs of hypercubes
Nana Arizumi, Peter Hamburger, and Alexandr Kostochka · 2008
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On 2-detour subgraphs of the hypercube
József Balogh and Alexandr Kostochka · 2008
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Fault tolerant additive and ( μ \mu , α \alpha )-spanners
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Merav Parter · 2017
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A hierarchy of lower bounds for sublinear additive spanners
Amir Abboud, Greg Bodwin, and Seth Pettie · 2018
Later among the works it cites.
Two results about the hypercube
József Balogh, Tamás Mészáros, and Adam Zsolt Wagner · 2018
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Distributed construction of purely additive spanners
Keren Censor-Hillel, Telikepalli Kavitha, Ami Paz, and Amir Yehudayoff · 2018
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Graph spanners: A tutorial review
Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, and Richard Spence · 2019
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Near-additive spanners in low polynomial deterministic congest time
Michael Elkin and Shaked Matar · 2019
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