Abstract
Introduction. In this paper the structure of graphs is studied by purely combinatorial methods. The concepts of rank and nullity are fundamental. The first part is devoted to a general study of non-separable graphs. Conditions that a graph be non-separable are given; the decomposition of a separable graph into its non-separable parts is studied; by means of theorems on circuits of graphs, a method for the construction of non-separable graphs is found, which is useful in proving theorems on such graphs by mathematical induction.
Presented to the Society, October 25, 1930; received by the editors February 2, 1931. An out·line of this paper will be ound in the Proceedings of the National Academy of Sciences, vol. 17 (1931), pp. 125-127.
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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC
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Whitney, H. (2009). Non-Separable and Planar Graphs*. In: Gessel, I., Rota, GC. (eds) Classic Papers in Combinatorics. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4842-8_2
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DOI: https://doi.org/10.1007/978-0-8176-4842-8_2
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