Kim, Seog-Jin; West, Douglas B. Triangle-free planar graphs with minimum degree 3 have radius at least 3. (English) Zbl 1172.05317 Discuss. Math., Graph Theory 28, No. 3, 563-566 (2008). 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.) Keywords:planar graph; radius; minimum degree; triangle-free; dominating set PDFBibTeX XMLCite \textit{S.-J. Kim} and \textit{D. B. West}, Discuss. Math., Graph Theory 28, No. 3, 563--566 (2008; Zbl 1172.05317) Full Text: DOI