Abstract
Our definition of k-connectedness, given in Chapter 1.4, is somewhat unintuitive. It does not tell us much about ‘connections’ in a k-connected graph: all it says is that we need at least k vertices to disconnect it. The following definition—which, incidentally, implies the one above—might have been more descriptive: ‘a graph is k-connected if any two of its vertices can be joined by k independent paths’.
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© 2017 Reinhard Diestel
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Diestel, R. (2017). Connectivity. In: Graph Theory. Graduate Texts in Mathematics, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53622-3_3
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DOI: https://doi.org/10.1007/978-3-662-53622-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53621-6
Online ISBN: 978-3-662-53622-3
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