Pure Pairs. IX. Transversal Trees

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-02-02 DOI:10.1137/21m1456509

Alex Scott, Paul Seymour, Sophie T. Spirkl

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 645-667, March 2024.
Abstract. Fix [math], and let [math] be a graph, with vertex set partitioned into [math] subsets (“blocks”) of approximately equal size. An induced subgraph of [math] is “transversal” (with respect to this partition) if it has exactly one vertex in each block (and therefore it has exactly [math] vertices). A “pure pair” in [math] is a pair [math] of disjoint subsets of [math] such that either all edges between [math] are present or none are; and in the present context we are interested in pure pairs [math] where each of [math] is a subset of one of the blocks, and not the same block. This paper collects several results and open questions concerning how large a pure pair must be present if various types of transversal subgraphs are excluded.

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纯对IX.横向树

SIAM 离散数学杂志》，第 38 卷第 1 期，第 645-667 页，2024 年 3 月。摘要固定[math]，设[math]是一个图，其顶点集被分割成大小大致相同的[math]子集（"块"）。如果[math]的一个诱导子图在每个块中正好有一个顶点（因此它正好有[math]个顶点），那么这个诱导子图就是 "横向的"（关于这个分割）。[math]中的 "纯对 "是[math]的一对互不相交的子集[math]，使得[math]之间要么存在所有边，要么没有边；在本文中，我们感兴趣的是纯对[math]，其中每个[math]都是其中一个块的子集，而不是同一个块。本文收集了一些结果和悬而未决的问题，涉及如果排除各种类型的横向子图，纯对必须有多大。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.