Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multicolor Ramsey Numbers for Complete Bipartite Versus Complete Graphs   Let H_1, ..., H_k be graphs. The multicolor Ramsey number r(H_1,...,H_k) is
the minimum integer r such that in every edge-coloring of K_r by k colors,
there is a monochromatic copy of H_i in color i for some 1 <= i <= k. In this
paper, we investigate the multicolor Ramsey number
$r(K_{2,t},...,K_{2,t},K_m)$, determining the asymptotic behavior up to a
polylogarithmic factor for almost all ranges of t and m. Several different
constructions are used for the lower bounds, including the random graph and
explicit graphs built from finite fields. A technique of Alon and R\"odl using
the probabilistic method and spectral arguments is employed to supply tight
lower bounds. A sample result is $c_1 m^2t/\log^4(mt) \leq
r(K_{2,t},K_{2,t},K_m) \leq c_2 m^2t/\log^2 m$ for any t and m, where c_1 and
c_2 are absolute constants.

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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga