Hamilton Cycles in Planar Locally Finite Graphs | Zendy

Henning Bruhn | Zendy; Xingxing Yu | Zendy

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Hamilton Cycles in Planar Locally Finite Graphs

Author(s) -

Henning Bruhn,

Xingxing Yu

Publication year - 2008

Publication title -

siam journal on discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.843

H-Index - 66

eISSN - 1095-7146

pISSN - 0895-4801

DOI - 10.1137/050631458

Subject(s) - mathematics , combinatorics , planar graph , discrete mathematics , compactification (mathematics) , unit circle , planar , graph , pure mathematics , computer science , computer graphics (images)

A classical theorem by Tutte ensures 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.

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