On the rainbow planar Turán number of paths

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-09 DOI:10.1016/j.disc.2025.114523

Ervin Győri , Ryan R. Martin , Addisu Paulos , Casey Tompkins , Kitti Varga

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引用次数: 0

Abstract

An edge-colored graph is said to contain a rainbow-F if it contains F as a subgraph and every edge of F is a distinct color. The problem of maximizing the number of edges among n-vertex properly edge-colored graphs not containing a rainbow-F, known as the rainbow Turán problem, was initiated by Keevash, Mubayi, Sudakov, and Verstraëte. We investigate a variation of this problem with the additional restriction that the graph is planar and we denote the corresponding extremal number by

{ex}_{P}^{⁎} (n, F)

. In particular, we determine

{ex}_{P}^{⁎} (n, P_{5})

, where

P_{5}

denotes the 5-vertex path.

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在彩虹平面上Turán路径数

如果一个边色图包含F作为子图，并且F的每条边都是不同的颜色，我们就说它包含彩虹F。在不包含彩虹- f的n顶点正确边彩色图中最大化边数的问题，称为彩虹Turán问题，是由Keevash， Mubayi， Sudakov和Verstraëte提出的。我们研究了这个问题的一个变体，附加的限制是图是平面的，我们用exP _ （n，F）表示相应的极值数。特别地，我们确定exP (n,P5)，其中P5表示5顶点路径。

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.