Hamilton Cycles in Planar Locally Finite Graphs
نویسندگان
چکیده
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 definition we prove a partial extension of Tutte’s result to locally finite graphs.
منابع مشابه
Hamilton circles in infinite planar graphs
A circle in a graph G is a homeomorphic image of the unit circle in the Freudenthal compactification of G, a topological space formed from G and the ends of G. Bruhn conjectured that every locally finite 4-connected planar graph G admits a Hamilton circle, a circle containing all points in the Freudenthal compactification of G that are vertices and ends of G. We prove this conjecture for graphs...
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 22 شماره
صفحات -
تاریخ انتشار 2008