Hamilton Cycles in Planar Locally Finite Graphs

Hamilton Cycles in Planar Locally Finite Graphs

A classical theorem by Tutte assures the existence of a Hamilton cycle in every finite 4-connected planar graph. Extensions of this result to infinite graphs require a suitable concept of an infinite cycle. Such a concept was provided by Diestel and Kühn, who defined circles to be homeomorphic images of the unit circle in the Freudenthal compactification of the (locally finite) graph. With this...

Infinite Hamilton Cycles in Squares of Locally Finite Graphs

We prove Diestel’s conjecture that the square G of a 2-connected locally finite graph G has a Hamilton circle, a homeomorphic copy of the complex unit circle S in the Freudenthal compactification of G.

Geodetic Topological Cycles in Locally Finite Graphs

We prove that the topological cycle space C(G) of a locally finite graph G is generated by its geodetic topological circles. We further show that, although the finite cycles of G generate C(G), its finite geodetic cycles need not generate C(G).

Geodesic topological cycles in locally finite graphs

We prove that the topological cycle space C(G) of a locally finite graph G is generated by its geodesic topological circles. We further show that, although the finite cycles of G generate C(G), its finite geodesic cycles need not generate C(G).

Hamilton Cycles in Planar Graphs and Venn Diagrams