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Tur'an's problem and Ramsey numbers for trees | Zhi-Hong Sun
; Lin-Lin Wang
; Yi-Li Wu
; | Date: |
12 Oct 2011 | Abstract: | Let $T_n^1=(V,E_1)$ and $T_n^2=(V,E_2)$ be the trees on $n$ vertices with
$V={v_0,v_1,...,v_{n-1}}$,
$E_1={v_0v_1,...,v_0v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}}$ and
$E_2={v_0v_1,...,v_0v_{n-3},v_{n-3}v_{n-2}, v_{n-3}v_{n-1}}$. In the paper,
for $pge nge 8$ we obtain explicit formulas for $ex(p;T_n^1)$ and
$ex(p;T_n^2)$, where $ex(p;L)$ denote the maximal number of edges in a graph of
order $p$ not containing any graphs in $L$. Let $r(Gsb 1, Gsb 2)$ be the
Ramsey number of the two graphs $G_1$ and $G_2$. In the paper we also obtain
some explicit formulas for $r(T_m,T_n^i)$, where $iin{1,2}$ and $T_m$ is a
tree on $m$ vertices with $Delta(T_m)le m-3$. | Source: | arXiv, 1110.2725 | Services: | Forum | Review | PDF | Favorites |
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