论文信息 - Imprimitivity of locally finite, 1-ended, planar graphs

Imprimitivity of locally finite, 1-ended, planar graphs

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 (2004) using graph-theoretical methods.

Jozef Sirán | Mark E. Watkins

[1] Carsten Thomassen,et al. 3-connected planar spaces uniquely embed in the sphere , 2002 .

[2] Heinz Adolf Jung,et al. A note on fragments of infinite graphs , 1981, Comb..

[3] Mark E. Watkins,et al. On the structure of infinite vertex-transitive graphs , 1977, Discret. Math..

[4] Jack E. Graver,et al. Locally finite, planar, edge-transitive graphs , 1997 .

[5] Jack E. Graver,et al. A characterization of infinite planar primitive graphs , 2004, J. Comb. Theory, Ser. B.

[6] H. Whitney. Non-Separable and Planar Graphs. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[7] Chris D. Godsil,et al. A note on bounded automorphisms of infinite graphs , 1989, Graphs Comb..

[8] Heiner Zieschang,et al. Surfaces and Planar Discontinuous Groups , 1980 .

[9] R. Halin,et al. Automorphisms and endomorphisms of infinite locally finite graphs , 1973 .

[10] Wilfried Imrich,et al. Separating double rays in locally finite planar graphs , 1995, Discret. Math..

[11] Bojan Mohar,et al. Tree amalgamation of graphs and tessellations of the Cantor sphere , 2006, J. Comb. Theory, Ser. B.

[12] H. Weyl. Permutation Groups , 2022 .

[13] G. Jones,et al. Theory of Maps on Orientable Surfaces , 1978 .

[14] Carsten Thomassen,et al. Planarity and duality of finite and infinite graphs , 1980, J. Comb. Theory B.