Optimal Adjacency Labels for Subgraphs of Cartesian Products

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-22 DOI:10.1137/23m1587713

Louis Esperet, Nathaniel Harms, Viktor Zamaraev

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2181-2193, September 2024.
Abstract. For any hereditary graph class [math], we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in [math]. As a consequence, we show that if [math] admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then so do the classes of subgraphs and induced subgraphs of Cartesian products of graphs in [math]. Our proof uses ideas from randomized communication complexity, hashing, and additive combinatorics and improves upon recent results of Chepoi, Labourel, and Ratel [J. Graph Theory, 93 (2020), pp. 64–87].

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笛卡尔积子图的最佳邻接标签

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2181-2193 页，2024 年 9 月。摘要。对于任意遗传图类[math]，我们为[math]中的子图类和笛卡尔乘积图的诱导子图类构建最优邻接标记方案。因此，我们证明，如果[math]允许满足信息论最小值的高效邻接标签（或等价于小型诱导通用图），那么[math]中的子图类和笛卡尔乘积图的诱导子图类也是如此。我们的证明使用了随机通信复杂性、散列和加法组合学的思想，并改进了 Chepoi、Labourel 和 Ratel [J. Graph Theory, 93 (2020), pp.］

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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.