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Ramsey numbers for trees II | Zhi-Hong Sun
; | Date: |
28 Oct 2014 | Abstract: | For $nge 6$ let $T_n^3=(V,E_1), T_n^{’’}=(V,E_2)$ and $T_n^{’’’} =(V,E_3)$
be the three trees with maximal degree $n-4$ given by
$V={v_0,v_1,...,v_{n-1}}$, $E_1={v_0v_1,...,v_0v_{n-4},v_1v_{n-3},$
$v_1v_{n-2},v_1v_{n-1}},
E_2={v_0v_1,...,v_0v_{n-4},v_1v_{n-3},v_1v_{n-2},v_2v_{n-1}},
E_3={v_0v_1,...,v_0v_{n-4},$ $v_1v_{n-3},v_2v_{n-2},v_3v_{n-1}}$. Let $r(G_1,
G_2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. 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
$T_nin{T_n’’,T_n’’’,T_n^3}$, $P_n$ is the path on $n$ vertices and $T_n’$ is
the unique tree with $n$ vertices and maximal degree $n-2$. | Source: | arXiv, 1410.7637 | Services: | Forum | Review | PDF | Favorites |
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