Infinite highly connected planar graphs of large girth |
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Authors: | A. Georgakopoulos |
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Affiliation: | 1. Mathematisches Seminar der Universit?t Hamburg, SP GD, FB 11, Bundestr. 55, 20146, Hamburg, Germany
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Abstract: | We construct infinite planar graphs of arbitrarily large connectivity and girth, and study their separation properties. These graphs have no thick end but continuum many thin ones. Every finite cycle separates them, but they corroborate Diestel’s conjecture that everyk-connected locally finite graph contains a possibly infinite cycle — see [3] — whose deletion leaves it (k — 3)-connected. |
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Keywords: | KeywordHeading" >2000 Mathematics Subject Classification 05C40 |
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