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problem for trees $T_n$ with maximal degree $n-4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yin-Yin Tu, Zhi-Hong Sun","submitted_at":"2014-10-27T15:52:00Z","abstract_excerpt":"For $n\\ge 6$ let $V=\\{v_0,v_1,\\ldots,v_{n-1}\\}$, $E_1=\\{v_0v_1,\\ldots,v_0v_{n-4},v_1v_{n-3},v_1v_{n-2}$, $v_1v_{n-1}\\}$, $E_2=\\{v_0v_1,\\ldots,v_0v_{n-4},v_1v_{n-3},v_1v_{n-2},v_2v_{n-1}\\}$, $E_3=\\{v_0v_1,\\ldots,v_0v_{n-4}$, $v_1v_{n-3},v_2v_{n-2},v_3v_{n-1}\\}$, $T_n^3=(V,E_1),\\ T_n^{''}=(V,E_2)$ and $T_n^{'''} =(V,E_3).$ In this paper, for $p\\ge n\\ge 15$ we obtain explicit formulas for $ex(p;T_n^3)$, $ex(p;T_n^{''})$ and $ex(p;T_n^{'''})$, where $ex(p;L)$ denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a 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