Abstract
A graph is a 1-dimensional simplicial complex. In this work we study an interpretation of “n-connectedness” for 2-dimensional simplicial complexes. We prove a 2-dimensional analogue of a theorem by Whitney for graphs:
Theorem (A Whitney type theorem for pure 2-complexes).Let G be a pure 2-complex with no end-triangles. Then G is n-connected if and only if the valence of e is at least n for every interior edge e of G, and there does not exist a juncture set J of less than n edges of G.
Examples ofn-connected pure 2-complexes are then given, and some consequences are proved.
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Woon, E.Y. n-connectedness in pure 2-complexes. Israel J. Math. 52, 177–192 (1985). https://doi.org/10.1007/BF02786514
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DOI: https://doi.org/10.1007/BF02786514