Cliques, Chromatic Number, and Independent Sets in the Semi-random Process

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-08-27 DOI:10.1137/23m1561105

David Gamarnik, Mihyun Kang, Paweł Prałat

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2312-2334, September 2024.
Abstract. The semi-random graph process is a single player game in which the player is initially presented an empty graph on [math] vertices. In each round, a vertex [math] is presented to the player independently and uniformly at random. The player then adaptively selects a vertex [math] and adds the edge [math] to the graph. For a fixed monotone graph property, the objective of the player is to force the graph to satisfy this property with high probability in as few rounds as possible. In this paper, we investigate the following three properties: containing a complete graph of order [math], having the chromatic number at least [math], and not having an independent set of size at least [math].

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半随机过程中的小群、色度数和独立集

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2312-2334 页，2024 年 9 月。摘要半随机图过程是一个单人游戏，在这个游戏中，玩家最初看到的是一个由 [math] 个顶点组成的空图。在每一轮游戏中，棋手会独立地、均匀地随机选择一个 [math] 顶点。然后，玩家自适应地选择一个顶点 [math]，并将边 [math] 添加到图中。对于固定的单调图属性，玩家的目标是在尽可能少的回合内迫使图以高概率满足这一属性。在本文中，我们将研究以下三个属性：包含秩为 [math] 的完整图、色度数至少为 [math]、没有大小至少为 [math] 的独立集。

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.