05885811

j

05885811 Changat, Manoj Mathews, Joseph Peterin, Iztok Narasimha-Shenoi, Prasanth G. $n$-ary transit functions in graphs. Discuss. Math., Graph Theory 30, No. 4, 671-685 (2010). 2010 University of Zielona G\'ora Press, Zielona G\'ora EN $n$-arity transit function betweenness Steiner convexity

doi:10.7151/dmgt.1522

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.