The relative degree and large complete minors in infinite graphs |
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| Institution: | 1. Health Economics Research Centre, Nuffield Department of Population Health, University of Oxford, Oxford, UK;;2. National Institute for Health Research Oxford Biomedical Research Centre, Oxford, UK;;3. Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford, UK.;1. Department of Econometrics and Operations Research, Tinbergen Institute, VU University, De Boelelaan 1105, Amsterdam 1081 HV, the Netherlands;2. Paris School of Economics, Centre d’Economie de la Sorbonne, CNRS, Université Paris 1, 106-112 Bd de l’Hôpital, Paris Cedex 13 75647, France |
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| Abstract: | Finite graphs of large minimum degree have large complete (topological) minors. We propose a new and very natural notion, the relative degree of an end, which makes it possible to extend this fact to locally finite graphs and to graphs with countably many ends. We conjecture the extension to be true for all infinite graphs. |
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