Faithful subgraphs and Hamiltonian circles of infinite graphs

2019/02/18 by Binlong Li, Li, Binlong
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1902.06402

openalex publication_date 2019/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A circle of an infinite locally finite graph G is the imagine of a homeomorphic mapping of the unit circle S¹ in |G|, the Freudenthal compactification of G. A circle of G is Hamiltonian if it meets every vertex (and then every end) of G. In this paper, we study a method for finding Hamiltonian circles of graphs. We illustrate this by extending several results on finite graphs to Hamiltonian circles in infinite graphs. For example, we prove that the prism of every 3-connected cubic graph has a Hamiltonian circle, extending the result of the finite case by Paulraja.

Citations

• Locally finite graphs with ends: a topological approach

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