One‐way infinite 2‐walks in planar graphs | Zendy

Biebighauser Daniel P. | Zendy; Ellingham M. N. | Zendy

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One‐way infinite 2‐walks in planar graphs

Author(s) -

Biebighauser Daniel P.,

Ellingham M. N.

Publication year - 2018

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22188

Subject(s) - combinatorics , mathematics , planar graph , bipartite graph , discrete mathematics , vertex (graph theory) , mathematical proof , graph , geometry

We prove that every 3‐connected 2‐indivisible infinite planar graph has a 1‐way infinite 2‐walk. (A graph is 2‐indivisible if deleting finitely many vertices leaves at most one infinite component, and a 2‐walk is a spanning walk using every vertex at most twice.) This improves a result of Timar, which assumed local finiteness. Our proofs use Tutte subgraphs, and allow us to also provide other results when the graph is bipartite or an infinite analog of a triangulation: then the prism over the graph has a spanning 1‐way infinite path.

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