Title: An upper bound for the planar Turan number of double star S_{3,5} Show Chinese title

Title: 关于双星树 \( S_\{\text\{{3,5}\}\} \) 的平面图Turan数的上界

Abstract: Given a graph H, the planar Turan number of H, denoted by ex_P(n, H), is the maximum number of edges in an n-vertex H-free planar graph. Ghosh, Gyori, Paulos and Xiao initiated the topic of the planar Turan number for double stars. A (k,l)-star, denoted by S_{k,l}, is the graph obtained from an edge uv, and joining end vertices with k and l vertices, respectively. However, the exact value of ex_P(n, S_{3,5}) remains unknown. Building upon this research, we further investigate the problem. A k-l edge refers to an edge whose endpoints have degrees k and l, respectively. In this paper, we establish an upper bound for the planar Turan number of a graph G that does not contain the double star S_{3,5} or any 6-6 edges, which is 23n/8 - 3 for all n >= 2. Show Chinese abstract

Abstract: 给定一个图 H，H 的平面 Turán 数，记作 ex_P(n, H)，是包含 n 个顶点且不含 H 的最大边数的平面图中的边数。 Ghosh、Gyori、Paulos 和 Xiao 开始研究双星的平面 Turán 数。 一个 (k,l)-星，记作 S_{k, l}，是从一条边 uv 出发，分别连接具有 k 和 l 个顶点的端点得到的图。 然而，ex_P(n, S_{3,5}) 的确切值仍然是未知的。 在此研究的基础上，我们进一步探讨了该问题。 一个 k-l 边是指其两端点的度分别为 k 和 l 的边。 本文中，我们为不含双星 S_{3,5}或任何 6-6 边的图 G 建立了一个上界，对于所有 n >= 2，该上界为 23n/8 - 3。