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广义饱和对策

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-05-15 DOI:10.1016/j.dam.2025.05.014

Balázs Patkós , Miloš Stojaković , Jelena Stratijev , Máté Vizer

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引用次数: 0

摘要

我们研究以下广义图Turán问题的博弈版本。对于两个固定的图F和H，两个玩家，Max和Mini，轮流要求完全图Kn的未被要求的边，这样要求的边的图G在整个游戏中必须保持F-free。游戏结束时，没有进一步的边可以要求，即当G成为f饱和。游戏的H值是H在g中的拷贝数。Max的目标是最大化H值，而Mini的目标是最小化H值。当两个玩家都处于最佳状态时，游戏的H值在Max开始时用s1（n,#H，F）表示，在Mini开始时用s2（n,#H，F）表示。我们研究了F和H的几种自然选择的这些值。

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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Generalized saturation game

We study the following game version of the generalized graph Turán problem. For two fixed graphs

F

and

H

, two players, Max and Mini, alternately claim unclaimed edges of the complete graph

K_{n}

such that the graph

G

of the claimed edges must remain

F

-free throughout the game. The game ends when no further edges can be claimed, i.e. when

G

becomes

F

-saturated. The

H

-score of the game is the number of copies of

H

G

. Max aims to maximize the

H

-score, while Mini wants to minimize it. The

H

-score of the game when both players play optimally is denoted by

s_{1} (n, # H, F)

when Max starts, and by

s_{2} (n, # H, F)

when Mini starts. We study these values for several natural choices of

F

and

H

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.