MacLane's planarity criterion for locally finite graphs

Authors:
Henning Bruhn;Maya Stein
Affiliations:
Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany;Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 8
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Abstract

MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B. Solving a problem of Wagner [Graphentheorie, Bibliographisches Institut, Mannheim, 1970], we show that the topological cycle space introduced recently by Diestel and Kuhn allows a verbatim generalisation of MacLane's criterion to locally finite graphs. This then enables us to extend Kelmans' planarity criterion as well.