Acyclic graphs with at least 2ℓ + 1 vertices are ℓ‐recognizable

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2023-08-22 DOI:10.1002/jgt.23027

A. Kostochka, M. Nahvi, D. West, Dara Zirlin

引用次数: 1

Abstract

The ‐deck of an ‐vertex graph is the multiset of subgraphs obtained from it by deleting vertices. A family of ‐vertex graphs is ‐recognizable if every graph having the same ‐deck as a graph in the family is also in the family. We prove that the family of ‐vertex graphs with no cycles is ‐recognizable when (except for ). As a consequence, the family of ‐vertex trees is ‐recognizable when and . It is known that this fails when .

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具有至少2个顶点的无环图是可识别的

顶点图的甲板是通过删除顶点从中获得的多个子图集。如果每个与族中的图具有相同甲板的图也在族中，则顶点图族是可识别的。我们证明了无环的顶点图族在（除）时是可识别的。因此，当和时，顶点树族是可识别的。众所周知，当。

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

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .