平面图中的等距子图守护和警察与强盗

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2024-06-01 DOI:10.1016/j.ejc.2023.103809

Sebastián González Hermosillo de la Maza, Bojan Mohar

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引用次数: 0

摘要

在 "警察与强盗 "游戏中，最有用的结果之一就是图中的等距路径可以由一个警察看守。在本文中，我们引入了子图中宽阴影的概念，并用它来描述所有可由 1 名警察看守的图。作为一个应用，我们证明了在任何平面图中，3 个警察都可以抓住一个劫匪，但附加的限制条件是最多有两个警察可以同时移动，这证明了杨的一个猜想，并加强了艾格纳和弗洛姆的一个经典结果。

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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Guarding isometric subgraphs and cops and robber in planar graphs

In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shadow in a subgraph, and use it to characterize all 1-guardable graphs. As an application, we show that 3 cops can capture a robber in any planar graph with the added restriction that at most two cops can move simultaneously, proving a conjecture of Yang and strengthening a classical result of Aigner and Fromme.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.