论文标题
PlanarTurán$ C_3 $和$ C_4 $的不交互式联盟数量
Planar Turán number of disjoint union of $C_3$ and $C_4$
论文作者
论文摘要
$ h $的{\ em planarturán编号}，由$ ex _ {\ mathcal {p}}}（n，h）$表示，是$ h $ free Planar Graph中的最大边数。 $ k \ geq 3 $ vertex-disjoint Cycles的平面Turán数量是一个微不足道的价值$ 3N-6 $。 LAN，SHI和SONG确定$ ex _ {\ Mathcal {p}}}}（n，2c_3）$的确切值。我们继续研究平面Turán循环的顶点 - 偶数联盟的数量，并获得$ ex _ {\ Mathcal {p}}}}（n，h）$的确切值，其中$ h $是$ C_3 $和$ C_4 $的Vertex-Disjoint Union。极端图也是表征的。当$ k $足够大时，我们还改善了$ ex _ {\ Mathcal {p}}}}（n，2c_k）$的下限。
The {\em planar Turán number} of $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $H$-free planar graph. The planar Turán number of $k\geq 3$ vertex-disjoint union of cycles is a trivial value $3n-6$. Lan, Shi and Song determine the exact value of $ex_{\mathcal{P}}(n,2C_3)$. We continue to study planar Turán number of vertex-disjoint union of cycles and obtain the exact value of $ex_{\mathcal{P}}(n,H)$, where $H$ is vertex-disjoint union of $C_3$ and $C_4$. The extremal graphs are also characterized. We also improve the lower bound of $ex_{\mathcal{P}}(n,2C_k)$ when $k$ is sufficiently large.
