图的结构化编码的相变

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-19 DOI:10.1137/23m1614572

Bo Bai, Yu Gao, Jie Ma, Yuze Wu

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引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷第 2 期，第 1902-1914 页，2024 年 6 月。摘要。我们考虑同一顶点集 [math] 上两个图的对称差，即 [math] 上的图的边集由恰好属于两个图之一的所有边组成。让[math]成为一类图，让[math]表示[math]上的图族[math]的最大可能心数，使得[math]中任意两个成员的对称差都属于[math]。阿隆等人最近研究了这些概念[SIAM J. Discrete Math.，37 (2023)，第 379-403 页]，目的是为编码理论提供一种新的图形方法。其中，[math] 表示这种编码的最大可能大小。现有结果表明，随着图类 [math] 的变化，[math] 可以从 [math] 变为 [math]。我们研究了一般情况下与 [math] 相关的几个相变问题，并提出了阿隆等人最近提出的一个问题的部分解决方案。

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Phase Transitions of Structured Codes of Graphs

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1902-1914, June 2024.
Abstract. We consider the symmetric difference of two graphs on the same vertex set [math], which is the graph on [math] whose edge set consists of all edges that belong to exactly one of the two graphs. Let [math] be a class of graphs, and let [math] denote the maximum possible cardinality of a family [math] of graphs on [math] such that the symmetric difference of any two members in [math] belongs to [math]. These concepts have been recently investigated by Alon et al. [SIAM J. Discrete Math., 37 (2023), pp. 379–403] with the aim of providing a new graphic approach to coding theory. In particular, [math] denotes the maximum possible size of this code. Existing results show that as the graph class [math] changes, [math] can vary from [math] to [math]. We study several phase transition problems related to [math] in general settings and present a partial solution to a recent problem posed by Alon et al.

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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.