关于传递图的弱cop数

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-12 DOI:10.1016/j.disc.2025.114559

Florian Lehner

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引用次数: 0

摘要

无限图的弱cop数可以看作是有限图的cop数的粗略几何类比。我们证明了每一个至少有一个厚端的顶点传递图都有无限个弱cop数。由此可见，每个连通的顶点传递图都有弱cop数1或∞，这回答了由Lee， Martínez-Pedroza和Rodríguez-Quinche提出的问题，并在最近由Appenzeller和Klinge，以及Esperet， Gahlawat和Giocanti的预印本中重申。

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On weak cop numbers of transitive graphs

The weak cop number of infinite graphs can be seen as a coarse-geometric analogue to the cop number of finite graphs. We show that every vertex transitive graph with at least one thick end has infinite weak cop number. It follows that every connected, vertex transitive graph has weak cop number 1 or ∞, answering a question posed by Lee, Martínez-Pedroza, and Rodríguez-Quinche, and reiterated in recent preprints by Appenzeller and Klinge, and by Esperet, Gahlawat, and Giocanti.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.