Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and Ramsey numbers for cycles and wheels   We study the structure of red-blue edge colorings of complete graphs, with no
copies of the $n$-cycle $C_n$ in red, and no copies of the $n$-wheel $W_n = C_n
\ast K_1$ in blue, for an odd integer $n$. Our first main result is that in any
such coloring, deleting at most two vertices we obtain a vertex-partition of
$G$ into three sets such that the edges inside the partition classes are red,
and edges between partition classes are blue. As a second result, we obtain
bounds for the Ramsey numbers of $r(C_{2k+1},W_{2j})$ for $k < j$ integers,
which asymptotically confirm the values of $4j+1$, as it were conjectured by
Zhang et al.

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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas