Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramsey numbers for trees II   Let $r(G_1, G_2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. For
$n_1\ge n_2\ge 1$ let $S(n_1,n_2)$ be the double star given by
$V(S(n_1,n_2))=\{v_0,v_1,...,v_{n_1},w_0,w_1,...,w_{n_2}\}$ and
$E(S(n_1,n_2))=\{v_0v_1,...,v_0v_{n_1},v_0w_0, w_0w_1,...,w_0w_{n_2}\}$. In
this paper we determine $r(K_{1,m-1},S(n_1,n_2))$ for $n_1\ge m-2\ge n_2$. For
$n\ge 6$ let $T_n^3=S(n-5,3)$, $T_n^{"}=(V,E_2)$ and $T_n^{'"} =(V,E_3)$, where
$V=\{v_0,v_1,...,v_{n-1}\}$,
$E_2=\{v_0v_1,...,v_0v_{n-4},v_1v_{n-3},v_1v_{n-2},$ $v_2v_{n-1}\}$ and
$E_3=\{v_0v_1,...,v_0v_{n-4},v_1v_{n-3},v_2v_{n-2},v_3v_{n-1}\}$. In this paper
we obtain explicit formulas for $r(K_{1,m-1},T_n)$ $(n>m+3)$, $r(T_m',T_n)$
$(n>m+4)$, $r(T_n,T_n)$, $r(T_n',T_n)$ and $r(P_n,T_n)$, where
$T_n\in\{T_n",T_n'",T_n^3\}$, $P_n$ is the path on $n$ vertices and $T_n'$ is
the unique tree with $n$ vertices and maximal degree $n-2$.

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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: hep-th