带禁忌扫帚的图形中的度数幂和星数

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-03 DOI:10.1016/j.disc.2024.114232

Dániel Gerbner

引用次数: 0

摘要

给定一个阶数为 d1，...，dn 的图 G 和一个正整数 r，设 er(G)=∑i=1ndir。我们用 exr(n,F) 表示无 n 个顶点的 F 图 G 中 er(G) 的最大值，用 ex(n,Sr,F) 表示无 n 个顶点的 F 图中星星 Sr 的最大数目。对于 r≥2、任意 ℓ,s 和足够大的 n，我们确定了 exr(n,B(ℓ,s))，证明了 Lan、Liu、Qin 和 Shi 的猜想。对于 r≥2、任意 ℓ,s 和足够大的 n，我们还确定了 ex(n,Sr,B(ℓ,s))。

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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Degree powers and number of stars in graphs with a forbidden broom

Given a graph G with degree sequence $d_{1}, \dots, d_{n}$ and a positive integer r, let $e_{r} (G) = \sum_{i = 1}^{n} d_{i}^{r}$ . We denote by ${ex}_{r} (n, F)$ the largest value of $e_{r} (G)$ among n-vertex F-free graphs G, and by $ex (n, S_{r}, F)$ the largest number of stars $S_{r}$ in n-vertex F-free graphs. The broom $B (ℓ, s)$ is the graph obtained from an ℓ-vertex path by adding s new leaves connected to a penultimate vertex v of the path.

We determine ${ex}_{r} (n, B (ℓ, s))$ for $r \geq 2$ , any $ℓ, s$ and sufficiently large n, proving a conjecture of Lan, Liu, Qin and Shi. We also determine $ex (n, S_{r}, B (ℓ, s))$ for $r \geq 2$ , any $ℓ, s$ and sufficiently large n.

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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.