The planar Turán number of Θ6-graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-08-04 DOI:10.1016/j.disc.2025.114709

David Guan, Ervin Győri, Diep Luong-Le, Felicia Wang, Mengyuan Yang

引用次数: 0

Abstract

There are two particular

Θ_{6}

-graphs - the 6-cycle graphs with a diagonal. We find the planar Turán number of each of them, i.e. the maximum number of edges in a planar graph G of n vertices not containing the given

Θ_{6}

as a subgraph, and we find extremal constructions showing the sharpness of these results - apart from a small additive constant error in one of the cases.

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Θ6-graphs的平面Turán号

有两种特别的Θ6-graphs -有对角线的6循环图。我们找到了它们中的每一个的平面Turán数量，即在不包含给定Θ6作为子图的n个顶点的平面图G中的最大边数，并且我们找到了显示这些结果的锐度的极值结构-除了其中一种情况下的小附加常数误差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.