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One-way infinite 2-walks in planar graphs. (English) Zbl 1391.05090

Summary: 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 C. C. Timar [Spanning walks in infinite planar graphs. Nashville, TN: Vanderbilt University (Diss.) (1999)], 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.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C40 Connectivity
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