Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Komlos Conjecture Holds for Vector Colorings   The Komlos conjecture in discrepancy theory states that for some constant K
and for any m by n matrix A whose columns lie in the unit ball there exists a
+/- 1 vector x such that the infinity norm of Ax is bounded above by K. This
conjecture also implies the Beck-Fiala conjecture on the discrepancy of bounded
degree hypergraphs. Here we prove a natural relaxation of the Komlos
conjecture: if the columns of A are assigned unit real vectors rather than +/-
1 then the Komlos conjecture holds with K=1. Our result rules out the
possibility of a counterexample to the conjecture based on semidefinite
programming. It also opens the way to proving tighter efficient
(polynomial-time computable) upper bounds for the conjecture using semidefinite
programming techniques.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys