• [Bab95] László Babai, Automorphism groups, isomorphism, reconstruction, Handbook of combinatorics, Vol. 1, 2, Elsevier Sci. B. V., Amsterdam, 1995, pp. 1447–1540. MR 1373683
• [Bab97] László Babai, The growth rate of vertex-transitive planar graphs, Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (New Orleans, LA, 1997) ACM, New York, 1997, pp. 564–573. MR 1447704
• [Bog08] Oleg Bogopolski, Introduction to group theory, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008. Translated, revised and expanded from the 2002 Russian original. MR 2396717
• [BW03] C. Paul Bonnington and Mark E. Watkins, Planar embeddings with infinite faces, J. Graph Theory 42 (2003), no. 4, 257–275. MR 1963100
• [CWY09] Qing Cui, Jian Wang, and Xingxing Yu, Hamilton circles in infinite planar graphs, J. Combin. Theory Ser. B 99 (2009), no. 1, 110–138. MR 2467822
• [DD89] Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989. MR 1001965
• [Die05] Reinhard Diestel, Graph theory, 3rd ed., Graduate Texts in Mathematics, vol. 173, Springer-Verlag, Berlin, 2005. MR 2159259
• [DK14] M. J. Dunwoody and B. Krön, Vertex Cuts, J. Graph Theory (2014), doi: 10.1002/jgt.21844.
• [Dro06] Carl Droms, Infinite-ended groups with planar Cayley graphs, J. Group Theory 9 (2006), no. 4, 487–496. MR 2243241
• [DSS98] Carl Droms, Brigitte Servatius, and Herman Servatius, Connectivity and planarity of Cayley graphs, Beiträge Algebra Geom. 39 (1998), no. 2, 269–282. MR 1642723
• [Dun] M. J. Dunwoody, Planar graphs and covers, Preprint available at http://www.personal.soton.ac.uk/mjd7/ .
• [Geo] Agelos Georgakopoulos, The planar cubic Cayley graphs of connectivity 2, European J. Combin. 64 (2017), 152–169. MR 3658826
• [Geo09] Agelos Georgakopoulos, Infinite Hamilton cycles in squares of locally finite graphs, Adv. Math. 220 (2009), no. 3, 670–705. MR 2483226
• [Geo12] A. Georgakopoulos, The Planar Cubic Cayley Graphs, Habilitationsschrift, Universität Hamburg, 2012.
• [Geo14] Agelos Georgakopoulos, Characterising planar Cayley graphs and Cayley complexes in terms of group presentations, European J. Combin. 36 (2014), 282–293. MR 3131895
• [GH15] A. Georgakopoulos and M. Hamann, The planar Cayley graphs are effectively enumerable, arXiv: 1506.03361.
• [Hoc13] W. Hochfellner, Hamilton-Kreise in kubischen planaren Cayley-Graphen, 2013, Master thesis, Technische Universität Graz.
• [Imr75] Wilfried Imrich, On Whitney’s theorem on the unique embeddability of $3$-connected planar graphs, Recent advances in graph theory (Proc. Second Czechoslovak Sympos., Prague, 1974) Academia, Prague, 1975, pp. 303–306. (loose errata). MR 0384588
• [Kro] B. Kron, Infinite faces and ends of almost transitive plane graphs, Preprint.
• [Mac67] A. M. Macbeath, The classification of non-euclidean plane crystallographic groups, Canad. J. Math. 19 (1967), 1192–1205. MR 0220838
• [Mit] K. Mitchell, Constructing semi-regular tilings, Talk given at the Spring 1995 Meeting of the Seaway Section of the MAA., http://people.hws.edu/mitchell/tilings/Part1.html.
• [Moh] B. Mohar, Personal communication.
• [Moh06] Bojan Mohar, Tree amalgamation of graphs and tessellations of the Cantor sphere, J. Combin. Theory Ser. B 96 (2006), no. 5, 740–753. MR 2236509
• [Sab58] Gert Sabidussi, On a class of fixed-point-free graphs, Proc. Amer. Math. Soc. 9 (1958), 800–804. MR 0097068, https://doi.org/10.1090/S0002-9939-1958-0097068-7
• [Whi32] Hassler Whitney, Congruent Graphs and the Connectivity of Graphs, Amer. J. Math. 54 (1932), no. 1, 150–168. MR 1506881
• [Wil65] H. C. Wilkie, On non-Euclidean crystallographic groups, Math. Z. 91 (1966), 87–102. MR 0185013
• [ZVC80] Heiner Zieschang, Elmar Vogt, and Hans-Dieter Coldewey, Surfaces and planar discontinuous groups, Lecture Notes in Mathematics, vol. 835, Springer, Berlin, 1980. Translated from the German by John Stillwell. MR 606743

References

• [Bab95] László Babai, Automorphism groups, isomorphism, reconstruction, Handbook of combinatorics, Vol. 1, 2, Elsevier, Amsterdam, 1995, pp. 1447–1540. MR 1373683 (97j:05029)
• [Bab97] László Babai, The growth rate of vertex-transitive planar graphs, Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (New Orleans, LA, 1997) ACM, New York, 1997, pp. 564–573. MR 1447704
• [Bog08] Oleg Bogopolski, Introduction to group theory, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008. Translated, revised and expanded from the 2002 Russian original. MR 2396717 (2009c:20001)
• [BW03] C. Paul Bonnington and Mark E. Watkins, Planar embeddings with infinite faces, J. Graph Theory 42 (2003), no. 4, 257–275. MR 1963100 (2004a:05040), https://doi.org/10.1002/jgt.10089
• [CWY09] Qing Cui, Jian Wang, and Xingxing Yu, Hamilton circles in infinite planar graphs, J. Combin. Theory Ser. B 99 (2009), no. 1, 110–138. MR 2467822 (2010e:05207), https://doi.org/10.1016/j.jctb.2008.05.002
• [DD89] Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989. MR 1001965 (91b:20001)
• [Die05] Reinhard Diestel, Graph theory, 3rd ed., Graduate Texts in Mathematics, vol. 173, Springer-Verlag, Berlin, 2005. MR 2159259 (2006e:05001)
• [DK14]M. J. Dunwoody and B. Krön, Vertex Cuts, J. Graph Theory (2014), doi: 10.1002/jgt.21844.
• [Dro06] Carl Droms, Infinite-ended groups with planar Cayley graphs, J. Group Theory 9 (2006), no. 4, 487–496. MR 2243241 (2007j:20061), https://doi.org/10.1515/JGT.2006.032
• [DSS98] Carl Droms, Brigitte Servatius, and Herman Servatius, Connectivity and planarity of Cayley graphs, Beiträge Algebra Geom. 39 (1998), no. 2, 269–282. MR 1642723 (2000a:05103)
• [Dun]M. J. Dunwoody, Planar graphs and covers, Preprint available at http://www.personal.soton.ac.uk/mjd7/ .
• [Geo] Agelos Georgakopoulos, The planar cubic Cayley graphs of connectivity 2, European J. Combin. 64 (2017), 152–169. MR 3658826, https://doi.org/10.1016/j.ejc.2017.04.005
• [Geo09] Agelos Georgakopoulos, Infinite Hamilton cycles in squares of locally finite graphs, Adv. Math. 220 (2009), no. 3, 670–705. MR 2483226 (2010b:05098), https://doi.org/10.1016/j.aim.2008.09.014
• [Geo12]A. Georgakopoulos, The Planar Cubic Cayley Graphs, Habilitationsschrift, Universität Hamburg, 2012.
• [Geo14] Agelos Georgakopoulos, Characterising planar Cayley graphs and Cayley complexes in terms of group presentations, European J. Combin. 36 (2014), 282–293. MR 3131895, https://doi.org/10.1016/j.ejc.2013.07.014
• [GH15]A. Georgakopoulos and M. Hamann, The planar Cayley graphs are effectively enumerable, arXiv: 1506.03361.
• [Hoc13]W. Hochfellner, Hamilton-Kreise in kubischen planaren Cayley-Graphen, 2013, Master thesis, Technische Universität Graz.
• [Imr75] Wilfried Imrich, On Whitney’s theorem on the unique embeddability of $3$-connected planar graphs, Recent advances in graph theory (Proc. Second Czechoslovak Sympos., Prague, 1974) Academia, Prague, 1975, pp. 303–306. (loose errata). MR 0384588 (52 #5462)
• [Kro]B. Kron, Infinite faces and ends of almost transitive plane graphs, Preprint.
• [Mac67] A. M. Macbeath, The classification of non-euclidean plane crystallographic groups, Canad. J. Math. 19 (1967), 1192–1205. MR 0220838 (36 #3890)
• [Mit]K. Mitchell, Constructing semi-regular tilings, Talk given at the Spring 1995 Meeting of the Seaway Section of the MAA., http://people.hws.edu/mitchell/tilings/Part1.html.
• [Moh]B. Mohar, Personal communication.
• [Moh06] Bojan Mohar, Tree amalgamation of graphs and tessellations of the Cantor sphere, J. Combin. Theory Ser. B 96 (2006), no. 5, 740–753. MR 2236509 (2007d:05047), https://doi.org/10.1016/j.jctb.2006.02.003
• [Sab58] Gert Sabidussi, On a class of fixed-point-free graphs, Proc. Amer. Math. Soc. 9 (1958), 800–804. MR 0097068 (20 #3548)
• [Whi32] Hassler Whitney, Congruent Graphs and the Connectivity of Graphs, Amer. J. Math. 54 (1932), no. 1, 150–168. MR 1506881, https://doi.org/10.2307/2371086
• [Wil65] H. C. Wilkie, On non-Euclidean crystallographic groups, Math. Z. 91 (1966), 87–102. MR 0185013 (32 #2483)
• [ZVC80] Heiner Zieschang, Elmar Vogt, and Hans-Dieter Coldewey, Surfaces and planar discontinuous groups, Lecture Notes in Mathematics, vol. 835, Springer, Berlin, 1980. Translated from the German by John Stillwell. MR 606743 (82h:57002)