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Triangle-free planar graphs with minimum degree 3 have radius at least 3. (English) Zbl 1172.05317

Summary: We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C12 Distance in graphs
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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