Abstract
We show that every set of \( m \simeq cn \sqrt {n log log n} \) vectors in {0, 1}n in which every vector has Hamming weight 3 contains a subset of {tiO(log n) vectors that form a linear dependency. Our proof is based on showing that in every graph of average degree at least c log log n, every legal edge coloring produces a cycle in which one of the colors appears either once or twice.} (In both results, c is some constant.) The results proved are used (in a companion work) in refutation algorithms for semirandom 3CNF formulas.
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© 2008 János Bolyai Mathematical Society and Springer-Verlag
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Feige, U. (2008). Small Linear Dependencies for Binary Vectors of Low Weight. In: Grötschel, M., Katona, G.O.H., Sági, G. (eds) Building Bridges. Bolyai Society Mathematical Studies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85221-6_9
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DOI: https://doi.org/10.1007/978-3-540-85221-6_9
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