On platypus graphs and the Steiner–Deogun property

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-07-04 DOI:10.1016/j.dam.2025.06.048

Carol T. Zamfirescu

引用次数: 0

Abstract

A platypus is a non-hamiltonian graph in which every vertex-deleted subgraph is traceable. We prove a series of results on platypus graphs. For instance, although there are planar platypuses and bipartite platypuses, it is not known whether there is a planar bipartite platypus. Motivated by this question, we show that every tree is an induced subgraph of some planar platypus. On the other hand, there exists an infinite family of planar graphs each member of which is not an induced subgraph of any planar platypus. Throughout the article we point out connections between platypus graphs and graphs having the Steiner–Deogun property, as defined by Kratsch, Lehel, and Müller.

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关于鸭嘴兽图和Steiner-Deogun性质

鸭嘴兽是一个非哈密顿图，其中每个删除顶点的子图都是可跟踪的。我们证明了鸭嘴兽图上的一系列结果。例如，虽然有平面鸭嘴兽和两肢鸭嘴兽，但不知道是否有平面两肢鸭嘴兽。在这个问题的启发下，我们证明了每一棵树都是某个平面鸭嘴兽的诱导子图。另一方面，存在一个无限的平面图族，其每一个成员都不是任何平面鸭嘴兽的诱导子图。在整篇文章中，我们指出了鸭嘴兽图和由Kratsch， Lehel和m ller定义的具有Steiner-Deogun性质的图之间的联系。

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

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.