A Non-aligning Variant of Generalized Turán Problems

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2023-02-25 DOI:10.1007/s00026-023-00640-8

Dániel Gerbner

引用次数: 0

Abstract

In the so-called generalized Turán problems we study the largest number of copies of H in an n-vertex F-free graph G. Here we introduce a variant, where F is not forbidden, but we restrict how copies of H and F can be placed in G. More precisely, given an integer n and graphs H and F, what is the largest number of copies of H in an n-vertex graph such that the vertex set of that copy does not contain and is not contained in the vertex set of a copy of F? We solve this problem for some instances, give bounds in other instances, and we use our results to determine the generalized Turán number for some pairs of graphs.

查看原文本刊更多论文

广义Turán问题的一个非对齐变量

在所谓的广义图兰数问题中，我们研究的是在 n 个无顶点 F 的图 G 中 H 的最大副本数。更确切地说，给定一个整数 n 以及图 H 和 F，那么在 n 个顶点图中，H 的最大副本数是多少，使得该副本的顶点集不包含且不包含在 F 副本的顶点集中？我们解决了某些情况下的这一问题，给出了其他情况下的界限，并利用我们的结果确定了某些图对的广义图兰数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches