Turán's problem for trees $T_n$ with maximal degree $n-4$

Abstract

For $n\ge 6$ let $V=\{v_0,v_1,\dots ,v_{n-1}\}$, $E_1=\{v_0{v}_1,\dots ,v_0{v}_{n-4},v_1{v}_{n-3},v_1{v}_{n-2}$, $v_1{v}_{n-1}\}$, $E_2=\{v_0{v}_1,\dots ,v_0{v}_{n-4},v_1{v}_{n-3},v_1{v}_{n-2},v_2{v}_{n-1}\}$, $E_3=\{v_0{v}_1,\dots ,v_0{v}_{n-4}$, $v_1{v}_{n-3},v_2{v}_{n-2},v_3{v}_{n-1}\}$, $T_n^3=(V,E_1),T_n^{{}^{\prime \prime }}=(V,E_2)$ and $T_n^{{}^{\prime \prime \prime }}=(V,E_3).$ In this paper, for $p\ge n\ge 15$ we obtain explicit formulas for $ex(p;T_n^3)$, $ex(p;T_n^{{}^{\prime \prime }})$ and $ex(p;T_n^{{}^{\prime \prime \prime }})$, where $ex(p;L)$ denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a subgraph.

28 pages

References in corpus (1)

• Turán's problem and Ramsey numbers for trees