The Induced Path Transit Function and the Pasch Axiom
نویسندگان
چکیده
The Pasch axiom is a strong geometric property which was noted and discussed even from the period of Euclid. Modern geometers followed the study of the Pasch axiom and in the context of axiomatic convexity this axiom was widely studied by pioneers in convexity theory. The connected graphs G for which the geodesic interval function I satisfies the Pasch axiom were characterized by Chepoi in 1994. In this paper, graphs for which the induced path transit function satisfies the Pasch axiom are characterized. Among arbitrary transit functions R that satisfy the Pasch axiom we identify the induced path transit function of the underlying graph GR by a set of axioms. M.S.C 2010: 05C75, 52A01, 51D20
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