论文标题
$ k_1p_ {2l} \ cup k_2s_ {2l-1} $的turán数字
The Turán number of $k_1P_{2l}\cup k_2S_{2l-1}$
论文作者
论文摘要
图$ h $的Turán数字，用$ ex（n，h）$表示，是$ n $顶点上包含no $ h $的任何图中的最大边数。令$ p_k $表示$ k $ dertices上的路径，$ s_k $表示$ k+1 $ dertices和$ k_1p_ {2l} \ cup k_2s_ {2l-1} $表示路径 - 斯塔尔森林，与$ k_1 $ p_ $ p_ p_ $ p_ a $ k_2 $ k_2 $ k_2 $ k_2 $ k_2 $ k_2 $ k_2 $ S_ {2L-1} S $。在2019年，Lan等人。确定$ ks_l $和$ k_1p_4 \ cup k_2s_3 $的Turán数字。 Zhang等人在2022年。确定了$ k_1p_6 \ cup k_2s_5 $的turán数字，并提出了turán数字的猜想，$ k_1p_ {2l} \ cup k_2s_ {2l-1} $，其中$ k_1 \ geqslant 1 $ and $ l \ geqslant 2 $。在本文中，我们研究了假设，并确定$ k_1p_ {2l} \ cup k_2s_ {2l-1} $的turán数字，当$ n $足够大。
The Turán number of a graph $H$, denoted by $ex(n, H)$, is the maximum number of edges in any graph on $n$ vertices containing no $H$ as a subgraph. Let $P_k$ denote the path on $k$ vertices, $S_k$ denote the star on $k+1$ vertices and $k_1P_{2l}\cup k_2S_{2l-1}$ denote the path-star forest with disjoint union of $k_1$ copies of $P_{2l}s$ and $k_2$ copies of $S_{2l-1}s$. In 2019, Lan et al. determined the Turán numbers of $kS_l$ and $k_1P_4\cup k_2S_3$. In 2022, Zhang et al. determined the Turán numbers of $k_1P_6\cup k_2S_5$ and raised a conjecture of the Turán numbers of $k_1P_{2l}\cup k_2S_{2l-1}$, where $k_1\geqslant 1$ and $l\geqslant 2$. In this paper, we study the hypothesis and determine the Turán numbers of $k_1P_{2l}\cup k_2S_{2l-1}$ when $n$ is sufficiently large.
