Watkins, Mark E.; Širáň, Jozef Imprimitivity of locally finite, 1-ended, planar graphs. (English) Zbl 1258.05051 Ars Math. Contemp. 5, No. 2, 217-221 (2012). Summary: Using results from group theory, we offer a concise proof of the imprimitivity of locally finite, vertex-transitive, 1-ended planar graphs, a result previously established by J. E. Graver and M. E. Watkins [Mem. Am. Math. Soc. 601, 75 p. (1997; Zbl 0901.05087)] using graph-theoretical methods. Cited in 1 Document MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C10 Planar graphs; geometric and topological aspects of graph theory 05C63 Infinite graphs 20B15 Primitive groups 20B27 Infinite automorphism groups Keywords:planar graph; primitive permutation group; residually finite group; co-compact group Citations:Zbl 0901.05087 PDFBibTeX XMLCite \textit{M. E. Watkins} and \textit{J. Širáň}, Ars Math. Contemp. 5, No. 2, 217--221 (2012; Zbl 1258.05051) Full Text: DOI