论文标题
通过禁止诱导子图I：网和公牛在本地有限图中强迫汉密尔顿性
Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs I: nets and bulls
论文作者
论文摘要
在一系列论文中，这是第一篇论文，我们研究了足够的汉密尔顿的条件，该条件是禁止诱导的子图，并将这些结果扩展到局部有限的无限图。为此，我们在局部有限图的佛教章节中使用拓扑圆圈作为无限循环。在本文中，我们将重点放在涉及爪，网和公牛的条件上，作为诱发的子图。我们将Shepherd的无爪和无净图形图扩展到局部有限图。此外，我们将Shepherd的无爪和无净图表分类为本地有限的图表。最后，我们延伸到本地有限的图表，这是Ryjáček涉及轻松的无牛的疾病。
In a series of papers, of which this is the first, we study sufficient conditions for Hamiltonicity in terms of forbidden induced subgraphs and extend such results to locally finite infinite graphs. For this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. In this paper we focus on conditions involving claws, nets and bulls as induced subgraphs. We extend Hamiltonicity results for finite claw-free and net-free graphs by Shepherd to locally finite graphs. Moreover, we generalise a classification of finite claw-free and net-free graphs by Shepherd to locally finite ones. Finally, we extend to locally finite graphs a Hamiltonicity result by Ryjáček involving a relaxed condition of being bull-free.
