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- W2166092110 abstract "Let X be a non-degenerate compact connected metric space. It is proved that if there is an n, 2 ⩽ n ⩽ ℵ0, such that X−A is not connected for all A ⊂ X of cardinality n, then X is a graph (that is, a one-dimensional compact connected polyhedron), and conversely. Furthermore, a formula involving only the edges and nodes of the graph X is found which calculates the smallest such n (which works for all A ⊂ X of cardinality n). As one of the consequences, it is shown that these are exactly five compact connected metric spaces for which the smallest such n is 3. A number of other results, as well as some new proofs of known theorems, are obtained." @default.
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- W2166092110 date "1993-02-01" @default.
- W2166092110 modified "2023-09-26" @default.
- W2166092110 title "Continuum Theory and Graph Theory: Disconnection Numbers" @default.
- W2166092110 doi "https://doi.org/10.1112/jlms/s2-47.1.167" @default.
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