密集电路图和循环的平面图兰数

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-08-08 DOI:10.1002/jgt.23165

Ruilin Shi, Zach Walsh, Xingxing Yu

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引用次数: 0

摘要

图的平面图兰数是一个无顶点平面图的最大边数。让表示长度为的循环。平面图兰数是已知的。我们证明了具有一定连通性的密集平面图（称为回路图）包含大的近三角形，并利用这一结果得到了平面图兰数的结果。特别是，我们证明存在一个常数，使得对于所有和。当这一约束严格到常数时，就证明了 Cranston、Lidický、Liu 和 Shantanam 的猜想。

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Dense circuit graphs and the planar Turán number of a cycle

The planar Turán number of a graph is the maximum number of edges in an ‐vertex planar graph without as a subgraph. Let denote the cycle of length . The planar Turán number is known for . We show that dense planar graphs with a certain connectivity property (known as circuit graphs) contain large near triangulations, and we use this result to obtain consequences for planar Turán numbers. In particular, we prove that there is a constant so that for all and . When this bound is tight up to the constant and proves a conjecture of Cranston, Lidický, Liu, and Shantanam.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .