Duality of ends

Authors:
Henning Bruhn;Maya Stein
Affiliations:
Mathematisches seminar, universität hamburg, bundesstraße 55, 20146 hamburg, germany (e-mail: hbruhn@gmx.net);Centro de modelamiento matemático, universidad de chile, blanco encalada 2120, santiago, chile (e-mail: mstein@dim.uchile.cl)
Venue:
Combinatorics, Probability and Computing
Year:
2010

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Abstract

We investigate the end spaces of infinite dual graphs. We show that there exists a natural homeomorphism * between the end spaces of a graph and its dual, and that * preserves the ‘end degree’. In particular, * maps thick ends to thick ends. Along the way, we prove that Tutte-connectivity is invariant under taking (infinite) duals.