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\(n\)-ary transit functions in graphs. (English) Zbl 1217.05081
Summary: \(n\)-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural \(n\)-ary generalization of geodesical convexity. Furthermore, we generalize the betweenness axioms to \(n\)-ary transit functions and discuss the connectivity conditions for the underlying hypergraph. Also, an \(n\)-ary transit function for all paths is considered.

MSC:
05C12 Distance in graphs
52A01 Axiomatic and generalized convexity
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